There are a lot of choices and much has changed over the course of several years
.It depends upon your budget though.If you're looking for a more expensive system (over $1,000 but generally $1,200 or more) many people here have switched to using quad core CPU's especially the super powerful Intel Core i7 920 CPU.
For a Intel inexpensive budget system the Intel Pentium E5200 Wolfdale 2.5GHz 2MB L2 Cache LGA 775 65W Dual-Core Processor is a good choice especially if you desire to overclock it in which case you will want an aftermarket heatsink for it.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116072
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Edit: Syzmek listed a great Intel combo deal.I didn't see his post before I posted.Good choice!
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If you are more familiar with AMD's CPU's on a inexpensive budget either of these Phenom II X2's (dual cores) would be fine although the 550 is better.
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=2010340343%201050748055&name=Phenom%20II%20X2
These CPU's have generally replaced the older and slower Athlon X2 line although there is now a Athlon II series now which is less powerful than the Phenom II X2's.
Some people have complained lately that AMD is including a cheaper heatsink and fan than what was included before (a decent copper heatsink and fan) on the Phenom II X2 CPU's.
Even better would be this tri core CPU which would perform better with multitasking and it's quite inexpensive as well.I think that this would be the best choice for you rather than the Phenom II X2's.This CPU is very popular.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103649
And you need a modern AM3 motherboard although these CPU's will work with many previous AM2+ motherboards but a BIOS update is most likely needed if you opt instead for a AM2+ motherboard.
The difference is that the older AM2+ motherboards use DDR 2 type of memory and current AM3 motherboards use DDR 3 memory.AM2+ motherboards will lose support eventually for future CPU's so if you desire to upgrade the CPU in the future it's best to stick with an AM3 type of motherboard.
There are many choices of AM3 motherboards but on a budget I like these types (they are new and inexpensive) and come with great Integrated Graphics.However you don't have to use the Integrated graphics as you can later add in a much better graphics card.
It's just that if you can't afford the discrete graphics card you will at least get the system up and going without out.
This board is micro-ATX sized so it will fit in a small case.Also it's so new I doubt at all that it would need any BIOS update for the X3 720 or the X2 550 CPU since these CPU's came out before this motherboard was released.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130233
Then you will need DDR3 type RAM for it.
Other people will give you suggestions as well.