I would recommend a dual core processor to building a computer now. Sadly, AMD CPUs are expensive at the moment (because they are in demand) so I would recommend to you a pentium chip. Don't worry if you think that intel is slower than AMD - it's not true. However, AMD chips have a small performance advantage in games but they command a high price premium for this.
Try tom's CPU charts to see the difference.
http://tomshardware.co.uk/cpu/charts.html?modelx=33&model1=323&chart=63&model2=328
Now, conroe (a new cpu) is coming at the end of July and iseems like it is going to be a big improvement on the current generation AMD/pentium chips. If you can't wait for conroe then here is the system I would recommend:
The Intel pentium 805 D. This is the slowest dual core processor there is but heck, games are not bottlenecked by the CPU these days. The reason why I recommend dual core is obvious once you start playing a game with them. They don't make your games go faster (not at the moment) but they make your computer feel far more stable. If you have a friend with one, ask them about it, have a play around with one.
http://www.newegg.com/Product/Product.asp?Item=N82E16819116001
$108.9
For the motherboard, try this Abit 975x motherboard. It should give you everything you need and is passively cooled. It doesn't support conroe though.
http://www.newegg.com/Product/Product.asp?Item=N82E16813127235
$176.99
One of the great things about this processor is that it can be overclocked extremely easily because its FSB speeds are set low by default. Bumping the FSB up to normal levels makes the CPU speed go sky high. There are two things to bear in mind with this, don't expect to go from 2.66GHz to 4GHz. It can be done but will not necessarily happen. Second, this will cause the CPU to run hot. Many people exaggerate the heat produced by this CPU as it is entirely managable and shouldn't be something to worry about.
If you plan on overclocking this CPU (and make it perform nearly as fast as an AMD FX-60/FX-62) try pruchasing a good heatsink and fan to go with the CPU. They aren't to expensive and often run quieter than the stock heatsink so you get another bonus with them.
Here's a good one:
The scythe mine
http://www.newegg.com/Product/Product.asp?Item=N82E16835185023
$44.99
But if you can find it, even better is the NH U-12
http://www.quietpc.com/us-en-usd/products/amdcooling/nh-u
$46.37
Goodluck, here's an article tom did on this processor (the processor's capabilities definately seem to be over estimated but it shows you how much of a bargin this processor is).
http://tomshardware.co.uk/2006/05/10/dual_41_ghz_cores_uk/