No Wii or PS2.
Never was a Tekken fan... ridge racer... maybe... I also plan to run ScrummVM not sure if that should determine my decision either. I plan to put in a GPU as well that will be sufficient but not sure what would be a good choice. I want to keep this build on a budget because I plan to sell it.
There isn't an X3 fast enough to run Ridge Racer.

I have a 2.9Ghz X3 in my primary setup, and a 3.4Ghz X3 in both my driving cab and new project. (have around $250 in each pc)
The 2.9Ghz one is just fast enough to run Carnevil and Tekken 3, but I've done a lot of tweaking in windows to save resources.
You'd probably be happy with a 3.2Ghz or 3.4Ghz one. I wouldn't recommend anything slower unless you have no interest in 3D games. (and the price difference is negligible)
It's fast enough to run a fair number of the 3D games including Tekken, Dreamcast on NullDC, Atomiswave on Demul, etc.
The X3's are toward the end of their life cycle, but I like them for budget builds because you can save money by buying a
90w 95w mobo and smaller power supply.
I recommended this setup last month to someone who wasn't sure what pc components to buy and they were thrilled with it.
That said, if you have a bigger budget, the Intel i5 2500k or faster is the way to go.