I was looking for cheap CPUs and I noticed the Intel Core i3-3225 3.3GHz.
It's $144.99 on Newegg.com
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116774It's the only i3 that has Intel HD Graphics 4000, which makes it kind of an oddball.
All the other i3 chips have Intel HD Graphics 2000/2500/3000.
Even though you won't use it for GroovyMAME, it might come in handy in the future if you re-purpose the PC for a home theater box or something.
It's an IvyBridge part.
It's only a dual core, but it supports hyperthreading, so it's like a ghetto quad core.
It supports DDR3-1333/1600 memory.
It's a 55W part (lower power means less less cooling needed).
If I was going to go with an i3, this is probably what I'd get.