I am just hoping that you do not play to Honest Abe's stereotypes. Nothing against him or this TL, but there were many interesting facts of note that would have defined his Presidency in a very different manner had he lived.
Can you tell me some things you would like to see in the TL?
Well, one thing that I found interesting was that by the time of his death, he was looking to relocate the African-American population of the South outside of the United States. Suggested locations ranged from Liberia, Santo Domingo, Haiti, Honduras, Ecuador, and even the Amazon. He was convinced that while African Americans were indeed entitled to the same rights as American citizens, they could not successfully assimilate into American society; however these plans dies with him, and the resulting power struggle between Congress and the Presidency. On this same note, he DID NOT desire the immediate emancipation of Slavery in the United States, despite the Emancipation Proclamation, which only effected territory still held by the Confederacy at that time.
Also, he wished to bring the South back as brothers, not a group that had committed any form of treason against the nation, so as to prevent any lasting wounds in relations between the regions. Basically, his plan was to grant amnesty to all those Southerners who would take an oath of loyalty to the Union, and agreed to follow the new federal laws in regards to slavery. High Confederate Officials would require Presidential pardons to receive their political rights back. When around 10% of a state's population took the oath of loyalty, they would be able to form a government and send Representatives to Congress. This was even more lenient than the policy suggested by Andrew Johnson.
There was also a growing animosity between Congress and the President, mostly because of the issues I have mentioned above, and likely would have fueled further troubles.
Off of the topic of Lincoln, there was fear within the Republican Party that the Democratic Party would be able to take control once the African American population was elevated to "full personhood". Up to that time, each had been considered "three-fifths of a person", under the said compromise. As a result of its end, the South would gain political power in Washington upon their return. These Southern Democrats would then, in their eyes, work to overturn what had already been accomplished over the course of the Civil War. This eventually came to pass, not through Washington, but through the individual states themselves, shortly after the military withdrawal a decade later.