I mainly use Chaos. If you want to try to mess with him, this is my bread-'n-butter combo when done right (although you're going to have to figure out what it means, because I completely forgot what acronyms PR uses for its high punch/low punch, low kick/high kick, etc).
Jump in -> low kick (while in air) -> down + both kicks (still in the air) -> (on the ground) punch -> down + fierce kick (he will do a sweeping motion with his hand while ducking) -> down + both kicks (he will trip the enemy) -> hold left punch + left kick and tap forward twice (this initiates his shoulder slam) -> down + both punches (he does a dual uppercut which will hit the enemy while they are still in the air).
Not sure if that makes any sense or not, but play around with it and see what you can do. To get used to that combo string, practice each part on its own. For instance, any time Chaos trips a character with down + both kicks, he can go straight into the shoulder slam then down + both punches combination. Some parts of the string require you to execute moves and other attacks faster than others, so experiment. If you watch my Let's Play video of the 3DO version (link: http://youtu.be/paHyu2KH_g0
), I probably manage to pull it off at least a couple of times. If you do it right, you will probably get the thunderbolts in the background along with the "wacky combo" label, or something like that. Primal Rage always makes it feel rewarding when you pull off a nice long combo.
I mainly stick with the apes when I play this game, with Chaos being my main character. Him and Blizzard are great for practicing combos with because they both have stun attacks (Blizzard with his freeze moves, and Chaos with his fart attack). I find Blizzard's combos more difficult because instead of the fast shoulder slam that seems to come out of nowhere, he has a wind-up punch he tosses out while lunging across the screen, depending on the strength of the attack used. Blizzard is probably a better beginner character though (he was my introduction to the game) because you can keep spamming the projectile freeze move as if you were playing as Sub-Zero in a Mortal Kombat game.
*edit: I do a shorter variation of that combo string above at around the 17:55 mark in my video. Timecode link straight to that part in the video: http://youtu.be/paHyu2KH_g0?t=17m55s