If you're using Litecoin then you're going to probably want a high-performance CPU with a low latency cache design and good overclockability, like an Intel i5 or i7. Intel's i5-2500k is a great choice and is what I use (not for mining though). If you're looking at going AMD then you may want to go for a Bulldozer based chip, as I believe it has extra integer processing power, and integer factorization is what bitcoin and litecoin both use for mining. I'm not very well versed in AMD's current lineup or tech so you may want to ask somebody else about that.
If you're mining regular bitcoins then CPU mining will be a huge waste of time a money. You'll want to run GPUs (video cards) or FPGAs hosted on a computer.
I myself run two full towers as dedicated 24/7 miners each with one GPU. The processors I use for both are Celeron 430 - http://ark.intel.com/products/29735/Intel-Celeron-Processor-430-%28512K-Cache-1_80-GHz-800-MHz-FSB%29
. They are only 35W TDP and so are low heat output and could even be run fanless if you have a large enough heatsink. You can get them on ebay for very cheap (that's where I got mine): http://www.ebay.com/itm/Intel-Celeron-430-SL9XN-Single-Core-Desktop-CPU-Processor-1-80GHZ-512-800-06-/150818847996?pt=CPUs&hash=item231d80fcfc
If you're running AMD board(s) - as others have said the Sempron 140 or 145 is a great choice and is what I use in another box that serves as a simple fileserver.
Hope that helps