Hmmm. Why not ask the "chick you're trying to nail" what kind of wine she likes?
White doesn't always = sweet. There are sweet reds as well.
Cheap wine usually tastes ... well, cheap. I'm not saying that some cheap wines aren't good, but you do get what you pay for at a certain level. Besides, how do we know what's cheap for you? When I was in my twenties I figured that $6-10 was cheap. Now, I'm more of a $25-30 is cheap kind of guy. I've been known to spend more.
FYI - Some women/chicks don't like sweet wine. My wife (who is a chick) doesn't like sweet wine at all. Except for dessert wine ... but that's hardly cheap (can be in the hundreds - but worth it if the chick is really, really hot like my wife.)