Don't really have enough info on your computer. Do you have an exact model, as we'll need to know what motherboard it has and hence if it has a PCI-Express X16 slot for upgrading, as well as what power supply it has.
If you do have a PCI-E x16 slot (the default standard now), then it all depends on how much you want to spend, but for value for money (and performance) you can't go past the ATI 48XX series, notably the Radeon 4850, with the new 5850 being released manufacturers will be flushing whats left of the inventories out of the slightly older 48XX series cards.
There are different types of RAM, the two main ones for performance cards are GDDR3 and GDDR5, the main different is that GDDR5 works at twice the frequency of GDDR3 (more accurately it transfers twice as much data per clock than GDDR3). So GDDR5 is faster, however you also need to look at the width of the memory bus.
In a nutshell, you can't gain much from memory specs as it depends on the actual GPU, but assuming you are a yank then a HD4850 will set you back around $120 with a $20 mail-in rebate, so $99 all up.
If thats too much, the next bet will be HD4830, which is around $85 and around 10% slower, failing that a Radeon HD4670 which is around $70 and around 25% slower than a 4830, failing that, a 4650 which is around $45 and around 15% slower than a 4670. Failing that, get a HD4350 which I've seen sometimes for $25.
Even the 4350 will be many times faster than your current (suspected) onboard graphics. But without more details, I can't give you much help.







