As noted already, upgrading the graphics card will be the single most effective upgrade. I would suggest something along the lines of a Radeon 7770 or nVidia GeForce 650 Ti for right around $100 in the US, not sure across the pond.
Be certain to check your systems power when doing so as the video card itself will be pulling about 150 watts MORE than your old card and this could overwelm your power supply requiring another upgrade.
Determining your budget after that would tell you the next upgrade. Assuming you have an open slot on the motherboard for more memory (or pulling a smaller chip to install new) would be the next most inexpensive upgrade, but upgrading the CPU might have more impact. You said you have 3 gigs now, so I am guessing you have two slots,, one with 2 gig and one with 1 gig. Purchasing a single 4gb stick and replacing the 1GB would be your best choice there and 6 gigs will be more than ample for you. Beyond that, look at what CPU's your motherboard can afford and purchase the best one you can get for your budget.