That question can be answered in about three volumes...
If your question is serious and not just fishing, the the mil standard ar15 will be 223/5.56 or some cartridge of length that will fit in the same size magazine. 308 will not.
A 308 will fit in an ar10 chambered in 308. There is no mil spec on the ar10 so you just have to make sure parts are compatible.
Best caliber? Depends on what you want it to do. Could easily take volumes to answer that.
I am looking at building a tool that fits the purpose of the second amendment, and of course some fun times at the range and out on the desert. Thank you for replying. It sounds like .556 fills the bill. Of course the lobbying by some random .556 fan on FR for years helps.