MGS1 is a DAMN good game

By fighting games I'd assume you really mean kung fu-like stuff and such, and not shooters and the likes, arcade stuff? If so, I'd recommend the Megaman X games. They have very good gameplay, still by its time nowadays, even if old.

I wonder why you don't want Resident Evil. Afraid of horror games? Heh heh

Anyway, I've played my favorite RPG - Chrono Trigger - on a SNES emulator (I should get an original copy somewhere) and this game is REALLY good. It's arguably one of the best RPGs ever in existence. But if I'm not mistaken they also made a PS1 version. If you like RPGs (and from the looks of it you like it), then you'd sure like Chrono Trigger, I tell you :) I'd even put my money on it, that you'd like it

More recommendations:
-Castlevania: Symphony of the Night.
-Tomb Raider?
-Tenchu: Stealth Assassins

That's all I can think of now.