First off, I don't have a PS3. I may get one in the future, but when the time comes for second console, it might be tough to choose between the PS3 and 360.
I'd suggest Ninja Gaiden Sigma. I haven't played it, but I did play Ninja Gaiden on X Box. It was easily one of the best games last gen. Now I hear you keep saying you don't like "cinematic" games, but by that do you mean games like Ninja Gaiden? In other words, games with a more realistic look? As far as story, NG wasn't very heavy with the story. If you hate games with lots of story, but could manage the 20+ minute cutscenes in MGS, the little story snippets shouldn't bother you. NG is very acradey, which is why I really want the series back where it belongs on a Nintendo console.
About Kingdom Hearts, I didn't like it the first time I played it either(about 2 hours). But then again I didn't like SSBM the first time I played it. Both were among my favorites last gen. Not trying to force it on you, but there's been too much KH bashing in this thread to not put my two cents in.
Since you're taking PS2 recommendations I'll mention a few others. Ico and Shadow of the Colossus. You say you think games are a horrible medium for story telling, but I think you may feel differently when you play Ico. It has one of the best and most moving stories in any game I've ever played. The amazing thing is it does this with minimal cutscenes and very few words spoken. The game itself is much fun with it's simple, yet appropriate combat, and emphasis on solving environmental puzzles that actually make sense(rather than just finding keys/crests and the usual suspects).
You want a fun, "casual"(I loath that word)game? Katamari Damacy. It's fun, simple, and quirky.
Hot Shots Golf 3. Simple enough to pick up and play, but deep enough to sink your teeth into. Some people are put off by the crazy/cute characters with the enormous heads, but I'm man enough to dig it. :) Of course, you may just want to get the one for the PS3 when you get the chance.
"I feel like I could take on the whole Empire myself."
