I'd like to see anouther 2d game.
Gba would be nice accually, The new crud like PS3 shouldn't be for it. Plus, most people aren't made of money.
Time period: right in the middle of JJ2. Say a side quest, that Jazz does. But, then you need to exsplain why there are no new weapons in JJ2:P
Game types: All of them, and maybe something like, the mini games you find in the game. (if you find them.)
Other companies: Who cares as long as it's good.
Cut-scenes:Just action scenes. Anything now with stories realy ruin the original games. (Sonic Heroes, yeah, realy messed things up.)