The games i would like to play are minecraft, left for dead 1&2, unreal tournement, GTA iv, world of war craft, call of duty b ops 2, garrys mod, arma 2 (dayZmod as well) and arma 3. Thanks btw i can play arma 2 on my dads non gaming computer and that was 400 and its not a good computer so don't say you need a £2000 computer to play it lol.
Budget of 600 and want to build a gaming computer?
Go to PCspecialist.co.uk and configure a PC there. It let's you see the price of your configured computer at the end and if it's too much you can go back and change the components. The end results are usually very good.
Mate you need to save up more money. For a good machine
http://uk.pcpartpicker.com/p/36W3Z
This one will give you the best price to performance issue. IT will be able to play all the games you listed with no problem. Heck, you could even play BF4 and Crysis 3 on high settings really well.
Ezio Auditore De Firenze made a great pc build for you, but it could be even better. All you have to do is go around school and ask any of your friends if you could barrow their windows disk and maybe offer them like $10 if they do not want to just let someone use it like that. This would allow you to spend more of your money on the actual hardware of your computer. This would leave you with a good extra $60 to spend. With that, I would recommend getting a amd fx-9370, which is a $300 cpu, but search for it in pcpartpicker where it is the cheapest. Even if you can't find anyone to lend you their copy of windows, I would still get this if you have the money because it is much more worth your money then a fx-8320. I would buy soon though because you have a really good deal right now in that build. That should allow you to play all of the games you listed on ultra settings. An optical drive is not a necessity for the beginning a a new build so you could just take it out of another pc and just use it to install windows and then put it back. Sop if you decide not to buy your own copy of windows go with the cpu and motherboard from this list. I just changed Ezio Auditore De Firenze's list around a little in this list. If you decide to buy windows, then go with Ezio Auditore De Firenze' lisst, but I wouldn't get the optical drive.
My listm: http://uk.pcpartpicker.com/p/36XH7
Ezio Auditore De Firenze's list": http://uk.pcpartpicker.com/p/36W3Z
I would recommend to join the two lists to suit your budget perfectly to your liking.