Lack off SSE2 has been the source of some compatibility breakage with Pentium 3 and Athlon CPUs. Most notably and unnecessarily with Steam, whose developers have a habit of compiling the launcher frontend with legacy hostile flags set. An ability to emulate SSE2 just to bypass such requirements would be pretty sweet, but at this point it doesn't seem like it's ever going to happen.
I remember reading some discussion about this idea, and it seemed like the main problem is that due to the way Intel implemented those instructions, it's problematic to trap them. I don't remember why that is, but I think that was the problem people were having with the idea.
I've tried running some silly things on a P3 just for the fun of seeing how it would handle it, but I did those things from XP. Getting the Steam launcher to run was the main problem I ran into, but at least at the time it was still possible. Surprisingly, Skyrim doesn't require SSE2, or if it does, then the requirement only kicks in rarely enough to just make you think the game crashes a lot.
Some simpler Indie games were quite playable, even though they generally did not list P3 as supported. Probably because they didn't have one to test, I imagine.
Graphics card - if you want the machine to attempt to run things that are much newer than the P3 era, then use a card that supports later features for better compatibility. If I've misinterpreted, then nevermind the following and just use something like an FX series or a Ti4200.
On my silly build, I used a 694X board as you are using, and used a 7600GS with it. The 7600GS allowed it to run semi-modern Indie games, but there were also some problems. The 7600GS is natively an Express GPU and relies on a bridge chip to communicate with AGP. My unconfirmed belief is that this type of card is not compatible with the 694X chipset. Some games ran fine, others had seriously broken rendering. I haven't yet confirmed the cause but I strongly suspect the bridge chip not getting along with the VIA 694X chipset. The card was definitely good, I had tested it thoroughly with a couple of later AGP chipsets without issue.
I haven't yet tried a 6800/GT/Ultra, but that's what I think is the best option - under XP at least. It should have similar feature/API support as the 7xxx series cards, but the 6800 GPUs are natively AGP so I think they should get along better with the VIA chipset. However, I have no idea what driver support exists for these cards under Win7.
The 6600 is *not* an answer - those are bridged again like the 7xxx family.
In terms of performance, older cards generally make more sense, but they won't be as compatible with future dated software that I think you might be trying to push the machine to run.
