Ah, memories...my first FF game for the PC...
Anyway, like most have said, it runs best in Glide. I tried to run it with the Direct3D patch back on my TNT2 (Viper V770 to be precise), but it would crash whenever I got to the overworld. So I gave up on it. More recently however, I've had a Voodoo2 flying around between systems for nothing more than Glide compatability (I'm surprised how well that card still works for UT!) and it's still best in Glide.
If you wanted a truly "cheap" card, with your fast setup, a Voodoo Banshee would probably do the job. Here's an idea if you're crazy enough (or just have a free PCI slot); put the PCI Banshee into your system along with your current ATi card. Get a splitter to run the monitor to both video cards. But disable multimonitor support in Windows. When you want to game with Glide, reboot your system, quickly change the BIOS setting to boot from AGP to PCI instead, and go. If you feel like changing back, just change the BIOS setting again.
It's a bit convoluted and may seem silly at first, but that's what I'm going to be doing very soon...otherwise just do what I originally did and get a Voodoo2 card.

If you've got a free PCI slot, it's a good little "tool" to have around for Glide emulation (Ultra64 anyone? I still play MarioKart64 from time to time...)