Yeah, what Mailpup said
Well, your internet is fine and it should play WoW with a better video card and more RAM. It probably won't play great, but it WILL play. Just some advice, try and stay out of BGs, major cities (ie. Ironforge, Ogrimmar), and 40-man raids. If get the RAM and video card it shouldn't lag in most places except the highly populated or graphic intensive ones.
Also, like the other guys said try and save up for a new PC too, you can get a pretty good one nowadays for cheap. You can get one with gaming specs for around $700 and throw in a good video card (ie. X850XT or 7600GT) for another $150 or around there. If you can't get a new one then you could probably make it run on your current computer.
Anyways, good luck
Tenko
Edit: Well, I've been looking around for decent PCI video cards and heres one that a guy is using that plays WoW at a steady 25 Fps which is pretty good.
Video Card
Also, the RAM will probably be between $70 and $100 also. If you want 1GB then maybe this would work?
RAM
It has good reviews and looks to be a pretty good product.
Edit2: Also, here is a basic picture of RAM
RAM Pic
and a basic video card pic
Video Card Pic
Edit3: If you are wondering how to install it, you basically just turn off your computer, turn off your outlet strip if you have one, open up your case, turn off your PSU's power switch, plug the RAM in, turn on your PSU power, close the case, and turn on the PC. Make sure you keep yourself grounded though. (To ground yourself you can either buy a anti-static wrist strap or you can just touch something that you think would shock you if you had a lot of static electricity (ie. iron door nob, metal fosset, etc.). This makes it so that when you touch your video card or any other parts it doesn't conduct the electricity into it and fry it.) Here is a tutorial on installing video cards
Tutorial and another one on how to install RAM
Tutorial. It would probably take a half hour, or an hour to install both items. The main thing though is to touch something metal every 20 or so minutes to keep yourself grounded.
Also, if you have any other questions just post them here and we'll try and help