Glad to hear that you're enjoying the game. TF2 has got to be one of the most entertaining online FPS that I've played in a looong time. I'll have to admit, seeing as I started my multiplayer FPS with TFC, I had my doubts about the cartoony look and all of the changes from TFC, but those reservations were unfounded.
In any respect, I'll second or third or whatever everybody's opinion that 2Fort is a good map to start out with. It's a classic CTF map and a TF2 staple. It's very balanced for all classes and a good map to hone your skills. But if you really want some competition, I think some of the best competition can be had on Dustbowl. It attracts a lot of regulars, and is where many of the top 50 (as ranked by our HLSX stats) play on a regular basis.