Which AMD Processor should i get?

I'd go for the Athlon II X4 640, since all of the rest of the CPUs in that list are also 3.0 GHz Athlon IIs and the X4 640 has the most cores. Current games will run about as fast on the Athlon II X3 440 as they do the X4 640 (and both will be notably faster than the X2 250) but games keep getting more multithreaded and the extra core in the X4 640 will be an asset in the not-so-distant future. Also, the price difference isn't that much between the X3 and X4, so go with the X4.

If the pricing is the same where you are as then UK the X3 is the best value by far and will equal the x4 in 9 out of 10 games. I also recommend getting the 1Gb 460 as long as it deosn't cost alot more

The OP said that budget is an issue, and an AMD platform is a better choice than anything Intel offers if you're not willing to spend >$300 on CPU and motherboard combined. I'm guessing the OP isn't willing to spend that much, else he would have CPUs like the Phenom II X4 Black Editions and X6s on that list instead of Athlon IIs. Also, there aren't any low-cost Sandy Bridge CPUs out yet, so anything in the price range of the M4A87TD + Athlon II will be either old Core 2-based stuff or a bottom-end LGA1156 unit like the Pentium G6950. Bulldozer-based parts won't be out until later this year, so if he needs a new and relatively inexpensive computer now, an Athlon II-based part would be the way to go right now.

As the others have stated the Athlon x4 would be the best choice for gaming and since it's utilizing 4 cores multitasking will be a breeze,and buying an AM3 motherboard will allow you to upgrade to the 1100T if the need arises.

Bunch of amateurs   Pfffft ...

Ultra-tight Budget Student Special

Sapphire Radeon HD 6850 1GB
Asus M4A78LT-M LE AM3

Sumthin' like that -- with the X3 Rana, Spinpoint F3 ($50-$60) & GeIL 4GB 2 x 2GB DDR3 1333. That's $392US.

And Students should not buy anything with the name "Gaming" in the title -- as in "Noble Gaming Casing". Students buy cheap cases, cut their fingers, strip some screws; snap, crack, dent and ding almost anything they touch. They also learn by trial & error, which is why they tend to buy cheap PSUs when advised to not do so.

So a fart smeller buys a solid PSU.

Spend the money saved on your GF --- and if you don't have a GF, you should not be investing in a computer, anyway. And if you are a girl, you 'Rock!' but leave now before these guys embarrass themselves any further