Computer Specs and Upgrades

Hi peopleI recently started playing League of Legends and noticed that my FPS was terrible (25fps at best)
i downloaded some program that showed me my computer specs.
i did a little research and found out that my computer had horrible specs.
for instance:2 RAM slots both 512mb and both DDR1 (both not surpassing 150mhz)
maximum capacity for memory is 2gigs
motherboard: intel pentium 4 CPU 2.40ghz
max CPU speed: 3060mhzmy video is pretty bad too
i have an ATI Radeon HD 2400 Series AGP
that has 512mb memoryOk. so what i would like to do is upgrade my PC so that i can run certain games decently. I am tired of having to choose which games i can play on this box.
I am not looking for Pro Gamer computers and such. I have a budget.I know i should replace my motherboard and videocard and upgrade my RAM for the best performance.
Does anyone have any suggestions as to how I can pick the right equipment?Thank you in advance.*PS. if you play league of legends too, add me @imChxrles

the whole computer needs replacing, essentially.

yeah i understand. i just want to know what i should upgrade it to.
i don't want to get something extreme. just sufficient

do an intel i3 build... should be sufficient enough
or a

Spoiler

Bulldozer build lol j/k

Replying to #4

bulldozer is far superior to i3. i3s are a complete waste of money. Intel hardware as a rule is hugely overpriced so if you're on a budget AMD are always the best option, you can get most of an AMD computer built for the same cost as an intel processor and motherboard, and AMD processors will equal anything except the top end i7s, which cost over $800 for the CPU alone.