Any of those would be able to run N64 & PS1.
It's a huge leap to PS2 & Wii. You need more of a current flagship processor like the fastest i5 you can afford.
Steer clear of the HP.
They aren't as reliable and the small form factor means trouble when you need to replace the power supply or video card.
You might also want to check out arrow direct.
http://arrowdirect.com/Always look for a discount code. Sometimes you can get a crazy good deal. Inventory changes regularly as new batches come off lease.
Last thing I got was a 3.2Ghz P4 with 1GB for $16.79 shipped.
I haven't seen many on there with video cards though.
If I were going to spend $300, I'd build my own from new parts.
EDIT: Not a dealbreaker, but having a 64-bit OS helps out with MAME. (demanding games are more likely to run full speed on a 64-bit OS)