Your system uses Socket A. Other than more ram it will be quite hard to track parts. I dont know if you can add a VGA card to the mix but it would be a strip down to the box and hard drive job. The best way to get a speed boost would be to sell what you have and buy something new. Even the lowest end of the market will be remarkably faster than what you have.
For what you want to do as a casual user ideally look for dual cores if you can afford it. If games are not important (Guessing not as you make no mention) then anything low end will do but do get a dedicated graphics card. Ram wise I would not worry if it is underspecified with say 256mb as £50 will get you 1gb with ease these days. Ideally get as much as you can afford to. Hard drive would be best catered for by getting at least a 200gb main one and maybe investing in a backup one either internal or external (320gb can be had for about £70 or less these days).
You can plausably get all that for about £600 obviously lowering specifications if you cannot afford that.