In no particular order...
Astro Boy (GBA)
An absolutely amazing game. I've had a blast with it, and even though the storyline and cameos probably won't make sense to you unless you're a fan of the source material (I'm not and they didn't), it's still a darn good platformer/shooter and one of the best GBA games I've played.
I need to finish it someday.
Sly Cooper And The Thevious Raccoonus (PS2)
Beautifully animated, good voice work, and a ton of fun to play. A bit frustrating at times (just wait until you get to the racing levels), but the sheer goodness of the rest of the (platforming and stealth) based game makes up for the few dull spots.
Ratchet & Clank (PS2)
Along with Sly Cooper, one of my favorite PS2 games. This has some platforming elements (notice a pattern here?
) but with a heavy emphasis on the guns and weaponry you pick up along the way. It reminded me of
Jet Force Gemini a lot, but since I've only got room for one on the list and because you've got some Ratchet sequels to play through too...well, the choice was obvious.
Legend Of Zelda: A Link To The Past (SNES)
There's a reason why this game is legendary. I have a feeling this one will do well in the rankings, and might win...which would be good, as it's probably one of the few "must play" titles that you could get a consensus on. Assuming you like RPGs (which I'd have to, going from the Final Fantasy games on your list), you won't regret this one at all.
And finally...well, I've never played this one (no Saturn), but I'd suggest giving...
Nights (Saturn)
...a shot. Again, the cult following is a sign that there's something there to warrant it, and I still haven't lost trust in Sega (though I have yet to play Shadow the Hedgehog, which might eradicate that by itself). Besides, I'd guess your Saturn doesn't get a ton of loving. Change that.
Since we're supposed to stick to five, don't count this as a vote, but remember one thing: you live in Ohio. If you're ever going to play
Boktai (GBA), do yourself a favor and start it while there's plenty of sun ahead of you. It's a good game, according to my sister; I can't speak for it myself, but I know how weather in the Midwest works and I think you might want to seize your chance.
Here's hoping you enjoy whatever we pick for you. Now, get out there and play something!