I'm very cheap... I always get as much for my dollar as I can... That doesn't mean I'll skimp on quality - I research major purchases carefully. Example, for the home theater, I got a system from Onkyo, rather than some crap sold at WalMart. Nonetheless, I called EVERY authorized online retailer to find the best shipped price to me... and I waited til the dealer with the best price also had a sale (free shipping and a decent % off.)
I'm not sure I really fit into any of your categories.... I think rather than calling myself "cheap", thrifty may be a better word.