Stock HS/Fan with the Semprons are really quiet. With budget being the concern, getting a dirt cheap cpu will let you afford more ram/larger hdd/nicer case/case of beer/etc.
If you're not gaming or encoding lots of video, the Sempy will probably be awesome for you.
Check this out! :
http://www.newegg.com/Product/Product.asp?Item=N82E16819104245
$40, Sempron 2800+ Socket 754, FREE SHIPPING
I use a Sempron 3100+ on an old NF3 mobo with a 128MB Radeon 9700 AIW as a spare HTPC, and can run everything I want on it easily, even have ram cobbled together, 1 512MB PC3200, 1 512MB PC2700. Quiet and competent and CHEAP!
Of course, if you require something faster, disregard my post

I just like to see people save money when they can!