If I'm not mistaken, a Barton 2800+ has 512K cache. That'll work even more better.
Maybe you can try at least AGP versions of 7300GT or 7600GS if you are going for the nVidia ones. Putting a 7800 will cause a serious bottleneck in the old machine.
If you want the ATi, go for the X1300 or the X1600 Pro. Both will do good in latest games, providing the settings not too maxed out.
I'm sure game framerates for your comp will be okay - 30~50 FPS I can guess if you have these video cards inside.
P.S: Try this - if you get the video card, and when you play the HL2 just in case - if you want to have good performance with better framerates, try to go inside the game settings, shut off the Anistropic Filtering and the Antialiasing. Then exit the game, right click and check the graphics settings in the desktop - try to play around with the AA and AF sliders and uncheck the "Application Controlled" box. I don't know - this will prevent conflicts. However, I would like some opinions about this, since I read this somewhere.
edit: Another one - I found out these HiS videocards for the x1300 Radeons - they are very optimized for the HL2 series. I haven't tried one of these yet.