Keeping in mind, that I will eventually want to reload for them, and currently have little or no real experience doing so, are any of these chamberings offered easier or harder to reload? Any problems to work around? Any idea on costs to reload for comparison? (I'm new to this)
.223 and .308 are both very easy to reload for. Biggest problem with both is too many good load combinations to choose from.
Wouldn't I need a AR-10 lower for .308?
Ah, too many threads, but yes, .308 is a different lower.
Additionally your instinct about the 5.56 being a good place to start is a good one.
Build a 5.56, play tinker toys with it, figure them out a bit, then go from there....