|Your system probably doesn't even have a video "card"...it probably has onboard video which is fine for just about everything else EXCEPT gaming. And you didn't bother to tell us how much RAM you currently have.|
I dug up the specs on your system. It supports dual channel DDR-SDRAM & has an 8X AGP slot. For decent gaming you should have at least 1GB of DDR400 (PC3200) as a matched pair (2 x 512MB). Just about any video card will be better than the crappy Intel Extreme graphics but for gaming, you'll need something fairly decent.
You're gonna have to decide how much you'll be willing to spend. Here's a few suggestions:
Dell™ Dimension™ 4600 Series Service Manual
Kingston ValueRAM 1GB (2 x 512MB) DDR400 (PC3200) Dual Channel Kit - $39
SAPPHIRE Radeon X1650PRO 512MB 128-bit GDDR2 AGP 4X/8X Video Card - $52
Open Box: SAPPHIRE Radeon HD3650 512MB 128-bit GDDR2 AGP 4X/8X HDCP Ready Video Card - $65