In reply to Ernest
Please see the following additional details:
Island is in the Caribbean, about fifty miles south and east of the southern tip of eastern Florida. It is about the size of Jamaica, so there would be plenty of room on this island to sustain this population.
Somehow, don't ask me how, it has remained uncharted, and hidden from the world. 
The island had no human habitation until a British ship drifted aground there about 500 years ago. The ship had men, women, and children aboard, headed for Guyana for a settlement. The passengers decided to remain on this beautiful island paradise, carried on through the generations, and are happy and content, although, only educated to the extent of 16th century standards, as this is what has been passed down through time. They live in houses built from wood found on the island.
The climate is of course like that of Jamaica or Cuba.
The population grows vegetables, and fruit grows plentifully naturally. They have cattle, chickens, hogs, geese, as the original ship brought seeds and livestock with them.
So these people would require major education to bring them into the 21st century.
Ugh. Given its location, I have to worry about Cuban and Haitian refugees, once word of the island gets out, which complicates matters.
Then there is the fact that early 16th-century Englishmen would be Catholics and wouldn't have even heard about the Reformation. On the other hand, their religion is probably primitive.Even if they'd had any priests aboard, I'm doubtful they'd have been able to maintain a formal church. The only Bible they probably would have had would have been a Latin Vulgate, and maybe not even that. (Unless it was a bunch of Lollards with a secreted Wycliffe Bible aboard the ship) It is entirely possible this utopia has done away with literacy, and even if they retain anything like it, I'm doubtful anyone knows Latin. So their religion is probably a folk religion with a basis in Christianity rather than anything remotely orthodox.
They might have gunpowder, but its probable that metalwork is rare and any steel is antique. Smithing is a sophisticated skill and with only 100,000 now, they probably started with at most 100 survivors, so it is doubtful they had a smith with them, and even if they did, they almost certainly had no smelters or miners (other than some hopeful gold miners). Free copper isn't too uncommon, but if they have anything better I'd be surprised.
You know, strike the idea of having to worry about Cuban and Haitian refugees. The only way a place like this even remotely makes sense given its location is if it is only accessible through a narrow transdimensional rift and I bought the location of it from its rediscoverer, so I can station a permanent guard ship or maybe even a fixed platform, to control access in and out of the island. (Or maybe the rift is only open every 500 years or so, but that would imply a totally different strategy.)
I'd start off my rule of this Bermuda Triangle Realm as Annatar, Lord of Gifts. Improved strains of agricultural staples, plus improved versions of the tools they already have would be what I would distribute in the first years of my rule, even as offshore oil platforms and deep sea fishing trawlers were deployed to pay for my largess. I'd also hire outsiders to help them relearn skills such as smithcraft and mining. As well as mercenaries to protect me in the event they aren't as amenable to my help as I would hope. I'd try to co-opt their existing structure as much as possible
My initial goal would be to get them up to a roughly 19th century level in technology within the first decade with literacy starting to catch on among the young. (I would not saddle them with the burden of learning Modern English, but would instead get them literate in their own language, since they would be able to have a phonetic spelling that way.)
By 2040, I'd hope to have them sufficiently prepared for the introduction of electricity and all that implies, including the radio and simple electronics. (Using transistors and not vacuum tubes. No need to duplicate every stage of our own development.) Electricity could probably be introduced earlier except I'd want to prevent them from interacting overmuch with the wider world until they were ready for it, so that means no electricity and no cell phones or internet until then.
