I am very excited about BioShock 3 as I enjoyed the first one (but didn't as much as other people because I knew the twist before even playing the game) and was amazed by 2. Its amazing gameplay is under-rated because of people's fondness of the original game I suppose. Anyway, I really want a bioshock 3, and as I see it, it could (and probably would) take place in one of two senerios. 
 
One-Take place as a prequel to Bioshock 1, or Two-Take place in the far future, in a rebuilt, self sustaining Rapture, discovered by NAVY SEALS (or maybe Russians). I'm wondering about which would be more interesting, and I wanna see your opinions. I think I'd pick the latter, as it would give us a most unfamiliar Rapture, and have that same sense of exploration as in the first game.

There are many possible scenarios. The game could be set on the surface. You could play as a soldier in Rapture, as you suggested. Or 2K could totally botch the thing by having you play as another Big Daddy shooting Splicers.

Prequel sequel.  Play as Andrew Ryan.  You can tickle 'em.  Confirmed.

I would be interested in a good side story. Maybe a prequel detailing the events of how Fontaine became Atlas. A prequel/sidestory would be great and add to the 'lore' that Bioshock has through all of the audio logs. Honestly, it was really hard to think of what Bioshock 2 was going to involve, but they did an excellent job. I hope they can pull another good idea from their sleeves for a trilogy and give the game lasting multiplayer.
 
I really want a full multiplayer suite. 10-12 player online, cooperative survival mode, and 2 player splitscreen with bots (1-4 splitscreen without bots for performance).