What would be the safest, fastest internet my computer is capable of? I currently have AOL 9.0 dial-up and it's slower than shit. Plus the computer is pretty slow when it comes to starting up and shutting down. (Windows XP)
Compaq
Intel(R)Celeron(TM)CPU
1300MHz
1.29 GHz
128 MB of RAM
OP, adding more RAM at that level should make a noticeable difference. I'm sure you could pickup a 128 or 256 stick of RAM fairly cheaply ($20?). If you're not sure, turn off the computer, open it up, obtain one of those anti-static bags, ground yourself to the case (just stay near it and touch the metal case a lot, while doing this), then remove the stick or sticks of RAM. Note how many RAM slots you have, also. Once the RAM is safely inside the anti-static bag, take it to your local computer shop and obtain their opinion on upgrading the RAM.
I don't know what you have for a motherboard, but simply obtaining a 256MB memory module should do it for most instances, but you might pursue some combination. The computer store will be interested in selling you as much RAM as possible, so be on your guard for being oversold. You want to get to at least 256MB of RAM, but 512MB is really pushing it, and anything over that is probably pure waste. Note well that you might be able to put in another stick of 128MB RAM and then test that out; if the machine seems to be quite a bit faster, then there's no need to get more; if not, then it's back to the computer store. (Just don't overbuy.)
You could help us here by opening the computer and then telling us how many memory slots you have, and what's in each. Hopefully your RAM modules have descriptive labels; write down everything you see on a label (but not what's written or embossed directly on the chips). If you can, try to identify what type of RAM you have; there are websites which can help you ID them (DDR, etc.).