If you could change three things in the US constitution...

[True Federalist (진정한 연방 주의자)]

What's with all the desire for PR for the House?  The size of the House would need to be considerably increased, well beyond a thousand, to have it work while keeping apportionment by States, and apportionment of the House by States is a minimal necessity for keeping our government a Federal one. For a country as large and diverse as ours is, a Federal system is a necessity, not merely a nicety.

Why? The federal government could easily organize federal elections without affecting the power of the states in other areas.

A Federal system needs its elected members to have ties to its local constituents, otherwise its constituent states have practically no way to impact Federal policy.  We already have a system that is too strongly tilted towards the central government as it is, no need to make it worse with a National PR system that would most likely lead to the abandonment of a Federal government and replace it with a National government.

As for why not PR by States, there are 7 States (8 if we give DC representation as a State that have only 1 Representative, and another 4 that have have only 2.  PR simply will not work as desired with those sorts of numbers.  If there were only one or two small entities as is the case in Italy, it would be less of a problem, but that is not the case with the US.

Now, as a compromise of sorts, tho I doubt few would care for it, which is why I didn't mention it my top 3, I could see returning the election of Senators to the State governments, in exchange for limiting its legislative functions to the approval of laws that directly impact State governments.  I.e., budgets to fund already authorized programs, and laws that do not affect State governments in any manner would only need approval by the House, but otherwise current Senate power would be unaffected. (i.e. confirmation of appointments, ratification of treaties, trying of impeachment cases, etc.)

[bedstuy]

1.  Call a constitutional convention for 2018.  Former President Obama heads it up.  Voting delegates would be: One person per state + 10 well-regarded Con Law professors + 10 Ex-SCOTUS or COA or State Supreme Court Judges + 10 smart people from various fields + any other ex-presidents who want in.  They get one year to propose 10 amendments.  There is a national vote on the amendments in 2019, popular vote. 

2.  Fix the Senate somehow.

3.  Kill the Electoral College.

[MyRescueKittehRocks]

1.Abolish the 16th Amendment
2. Abolish the 17th Amendment
3. Abolish the 23rd Amendment (DC voters considered as citizens of Maryland and thus receive congressional reps)

[Okay, maybe Mike Johnson is a competent parliamentarian.]

1. National popular vote and national standards for all federal elections, including IRV, possibly some form of MMP for the House, and paper trails
2. Make the Senate something closer to a revising chamber
3. No Second Amendment; Congress and the several states have plenary power over licenses for guns just as over licenses for any number of other things.

[tmthforu94]

End woman's suffrage.

[True Federalist (진정한 연방 주의자)]

End woman's suffrage.

Nah.  Let's end men's suffrage as well and let the robots rule.  Al Gore deserves a chance after all.

[H. Ross Peron]

1. Right to Life Amendment
2. Line Item Veto
3. Abolish EC

[True Federalist (진정한 연방 주의자)]

1. Right to Life Amendment

So you'd abolish the death penalty and establish a right to government provided health care?

[politicus]

A Federal system needs its elected members to have ties to its local constituents, otherwise its constituent states have practically no way to impact Federal policy. 

You already have the Senate for that + the vast majority of congressmen would still be elected by constituencies placed within one state.

As a compromise you could do FPTP in the smallest states, it wouldn't affect the overall result of elections that much.

[Orser67]

1)Have the Senate be elected by proportional representation at the national level. Keep the House the same.
2)Have all campaigns for federal offices be publicly-financed (using something along the lines of Ackerman-Ayres). Outlaw the direct participation of corporations in politics. Continue to allow individuals to donate money to PACs that are tied to issues (but not candidates), with a $10k max donation limit per year per person.
3)Give the federal government the power to make any laws that state governments can make.

[afleitch]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

[Franzl]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

[afleitch]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

Congress shall make no law respecting an establishment of religion, prohibiting the free exercise or repudiation thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

[Franzl]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

Congress shall make no law respecting an establishment of religion, prohibiting the free exercise or repudiation thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

I'm not opposed to your change of language, but I'm not aware of Congress attempting to prohibit the repudiation of religion?

[True Federalist (진정한 연방 주의자)]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

Congress shall make no law respecting an establishment of religion, prohibiting the free exercise or repudiation thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

I'm not opposed to your change of language, but I'm not aware of Congress attempting to prohibit the repudiation of religion?

Besides,  the existing First Amendment is already being interpreted by the courts as protecting the rights of atheists.

[Supersonic]

1. The Presidential system would be replaced by a parliamentary one
2. The election of the House of Representatives through PR FPTP
3. The second amendment would be worded far less categorically.

This. Except with election via FPTP.

[Sol]

1. Popular Election of the president
2. Significant revamping of the house:
-All Congressional districts must be drawn with deference to communities of interest, and population only,
-The party that wins the nationwide popular vote gets a bonus of 450 extra representatives.
-The House shall have 1255 members.
3. Abolish the Senate.

[Starbucks Union Thug HokeyPuck]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

Congress shall make no law respecting an establishment of religion, prohibiting the free exercise or repudiation thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

I'm not opposed to your change of language, but I'm not aware of Congress attempting to prohibit the repudiation of religion?

Besides,  the existing First Amendment is already being interpreted by the courts as protecting the rights of atheists.

No sir.  Its being interpreted (most of the time) exactly how it was meant to be implemented, to protect EVERYBODY from religion. 

[Okay, maybe Mike Johnson is a competent parliamentarian.]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

Congress shall make no law respecting an establishment of religion, prohibiting the free exercise or repudiation thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

I'm not opposed to your change of language, but I'm not aware of Congress attempting to prohibit the repudiation of religion?

Besides,  the existing First Amendment is already being interpreted by the courts as protecting the rights of atheists.

No sir.  Its being interpreted (most of the time) exactly how it was meant to be implemented, to protect EVERYBODY from religion. 

...which includes protecting the rights of atheists. Nobody said it's only protecting the rights of atheists; it's also interpreted to protect religions from other religions, or from the government.

It was not, however, always interpreted as it now is by courts past to the best of my understanding, and if afleitch is concerned that the interpretation may swing that way again at some point in the future I don't think that that concern is entirely unreasonable.

[Starbucks Union Thug HokeyPuck]

1. Enact Equal Rights Amendment extending protections to women and LGBT.
2. Scrap the 2nd Amendment empowering local jurisdictions to enact laws.
3. Tighten 'Freedom of Religion' to ensure that freedom from religion is protected in the public sphere.

What exactly do you have in mind for number 3?

Congress shall make no law respecting an establishment of religion, prohibiting the free exercise or repudiation thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

I'm not opposed to your change of language, but I'm not aware of Congress attempting to prohibit the repudiation of religion?

http://answers.usa.gov/system/selfservice.controller?CONFIGURATION=1000&PARTITION_ID=1&CMD=VIEW_ARTICLE&ARTICLE_ID=10053&USERTYPE=1&LANGUAGE=en&COUNTRY=US

http://nationaldayofprayer.org/

http://en.wikipedia.org/wiki/Religious_qualifications_for_public_office_in_the_United_States (14th Amendment, anybody?)

Thankfully we have the judicial system to do what it can... 

[DemPGH]

1) Echo what afleitch said about the right to repudiate religion
2) Establish a clear right to organize / unionize labor
3) Since modern gun violence is a relatively contemporary issue, I would clarify the second amendment to not impede gun regulation.

[RI]

There are so, so many things, but I'll try to pick 3:

1. Unicameral legislative branch consisting of the House of Representatives elected by instant runoff voting
2. Repeal of 10th Amendment and the dissolution of states as non-federally controlled units
3. Right to life amendment banning abortion, death penalty

[H. Ross Peron]

1. Right to Life Amendment

So you'd abolish the death penalty and establish a right to government provided health care?

I oppose death penalty in most cases FWIW and Obamacare seems to have mostly taken care of the second problem.

On second thought, I might replace abolishing the EC with an amendment mandating that Congressional district lines be drawn by a nonpartisan commission along with some at-large seats to be apportioned proportionally.

[Wake Me Up When The Hard Border Ends]

1. Mandate Congressional districts be drawn by a non-partisan commission at the federal level. States would still be free to draw their state-level districts however they please.

2. Repeal the 16th Amendment.

3. Right to Life Amendment.

There are many others though.

[Oldiesfreak1854]

There are plenty of things I would want to change, but here are a few:

1. Limits on the Tenth Amendment (not necessarily get rid of it, but have some changes)
2. Right to Life and/or Personhood Amendment
3. Amendment defining marriage as between a man and a woman, but allowing civil unions

I would mention having nonpartisan commissions draw congressional districts (and possibly state legislative districts), except that is probably something that should be enacted by the state legislatures rather than a constitutional amendment, since I can't recall anything in the Constitution that addresses this issue.  But if all else fails, I would go ahead with it.