I have a p4 1.8ghz 256mb system with intel integrated graphics. I sometimes play this game in which my average fps is around 20-30. Would it drastically increase my fps if i upgraded my memory to 512mb or do you recommend getting a 64mb graphics card? Also which has an higher impact on fps, sheer memory or processing power? for example adding 256 mb of ram or getting a graphics card which has a built in processor.

If you already have sufficient system memory, adding more wont do much. But a faster CPU will allways raise the FPS. And yes, the card would be a good idea, since it has its own GPU and RAM.

I normally agree that up grading your card would be the best thing to do to see the performance but in this case I'm not sure, it would really depend on the games your trying to play. Although I better video card does have it own graphics processor the card still relies on your RAM and if your lacking in RAM then even the best video card there is will have some problems. I personal would suggestion if I'm right about your PC spec: 32MB Video Card, 256MB Ram? If I' right about this setup and you decided to upgrade your video card than I wouldn't go any higher than a Geforce 4, card higher than this would need a new motherboard as well. But in my personal option you do also need to add more RAM. I would suggest at least having 512MB.

256 MB RAM can handle 128MB video card in most cases. if you wanna buy 64MB vidoe card, then i think that it's not vital to buy more RAM too. 256 is enough for most users. of course it'll always be better if you have more RAM, but if you have to chose between buying a new VC, or buying RAM i'd suggest you to buy the VC.

Oh, i've forgot something... what's you ram ? DDR ? and what's it's frequency ? you didn't mentioned none of this

ok ok ok, let the REAL nerd into this one!! now low fps is very common If you are going to buy a new upgrade considering FPS, go for video.. I recommend the Radeon9600xt. It is 128mb and it owns all Nvidia 128 cards by a big skip and a leap ($200 in price) it is TOTALY worth it because, 1) it kills all other 128mb videocards on the market 2) it is bundled with HalfLife2 (w00t). You may not have to get a new motherboard to support a new videocard as it seems that your comp is fairly new. As long as you have an AGP slot you can support it. I hope you know what an AGP slot is. If you dont, just say so. THE MOST IMPORTANT THING IN RAISING FPS IS LOWERING YOUR GAME RESOLUTION!! THIS WILL HELP EXTRAVAGENTLY!! Just go into the game options, look for video and/or resolution. It will probably be set at 1024x768 you want to set it down to 640x480 this will help GREATLY!! By doing this it will lower the number of pixels your CPU and VIDEOCARD have to deal with, creating higher FPS. ;-)

Graphics card is the most important, ram a lot less so and as long as your processor is in the GHZ range it should be fine.
also try and get the best drivers for your graphics card.