It's going to be a bit tough finding something that would fit ALL of those categories, and at that price. Here are a few suggestions that meet some of them. Most of them should be able to be found SOMEWHERE around your price range. Many of these can be fast enough to be fun to drive, some can actually make some really good power... it depends on what is fast to you.

Toyota MR2 Turbo
Eclipse GST / GSX (not the most reliable things)
Galant VR4 (same as above)
Dodge SRT4
Misc. Hondas (Civic, Integra) with B16s or B18s
Older Subaru WRXs

These may or may not be the best suggestions, but they would be the first things that come to mind.

My suggestion would be to browse the for sale section on this forum and see what you can dig up.