Just had a look.
The processor you're looking at isn't compatible with that motherboard...the CPU is socket 775 and the motherboard is 1156 (new intel i5) and it also takes DDR3 memory - which you may not have?
If you have DDR3 memory in your system at the moment then you could buy this processor:
http://www1.hardwareversand.de/articledetail.jsp?aid=27949&agid=1300it is a lot faster than the one you were looking at and should be fine with TF2/MW2 etc. And it is still just within your budget.
If you don't have DDR3 memory you will either need to buy some (putting you over your budget) or go for a Socket 775 motherboard, something like this perhaps?
http://www1.hardwareversand.de/articledetail.jsp?aid=26108&agid=659If you spend a little less on the motherboard - you might be able to get a better deal in terms of what CPU you can get and get a faster one.
Or perhaps something like this one:
http://www4.hardwareversand.de/articledetail.jsp?aid=27882&agid=659I think the Intel P45 chipset is one of the best performing ones you can get so try to look for a motherboard with that.