Not much you can do with that PC. I would bump the speed hacks right up to full - you're going to get graphics corruption here and there because of it like in the Calm Lands and Mushroom rock road and the High road especially with VU cycle all the way up but you can turn it down a notch when you need to.
And yeah software mode is the only way you're going to be able to do it. The only other thing is to change the sound settings and put them as low as possible and click disable effects processing.
Also of course run in native mode and maybe even in a window.
You're going to still have some serious slowdown in places namely some of the spells like Demi and some of the summons like Shiva so set the option in the game itself for summoning to short (which I think you can do in that game) and only the first time you summon will be the full length.
Once you get out of Zanarkand things should improve a bit especially once you pass all the beginning garbage and finally make it to the beach in Besaid.
In the end though your computer just isn't powerful enough but with these changes hopefully you can get a bit of a speedup