ATX S7/SS7 boards aren't very common where I live either, I have a Tyan Turbo S1573 that is technically only an S7 board but runs a K6-2 400 fine at FSB 66MHz and I'm content with it. I guess I should consider myself lucky.
Yes, that card is a YMF-719 and will suit you fine.
The other card is a Vortex 2, but there are better Vortex 2 cards out there; I would strongly suggest you go for one with a Wavetable header.
The wavetable header is one thing that makes it better than Live for me, the other is that its DOS drivers are a hundred times more compatible and its SB Pro emulation sounds a lot better than Live's SB16 emulation. They both have soft synths, Live has the upper hand here by using SF2s and not having a soundbank size limit, but for a PII you would be CPU limited in using large sound banks (say over 32MB). The default 4MB Vortex2 soundbank is roughly equivalent to Live's default 4MB sound bank, but inferior to the 8MB one and to some of the very nice larger soundbanks like General User, Unison, Merlin etc. Vortex2 supports A3D, Live supports EAX. A3D is superior and sounds a lot better, and is also a lot more contemporary and relevant to P2/P3 era games.
TNT2 Ultra would be more contemporary for that system, but is slower than the GF2MX which is roughly the same speed as a GF 256 which is usually outrageously expensive to get. I use a GF2GTS in my P3-700 build but I think it would not make a difference over a GF2MX with a Klamath 300. If you want to stick to nVidia, GF2MX will serve you well with this build. I skipped the early GeForce era with a Voodoo 3 3000 before eventually upgrading to a GF2 Ultra, but my sister's Celeron 400 system got a GF2MX at the same time and I remember it was a very nice match for that CPU and will complement a Klamat 300 well. Just don't expect high res 32-bit gaming with it, that card was usually paired with low end 15" monitors for 800x600 gaming, at best.
Retronautics: A digital gallery of my retro computers, hardware and projects.