In reply to tomholdenoid: just keep climbing, don't do anything too structured yet - just have fun and try lots of things. Maybe read up on some techniques (flagging, drop knees, finding rests etc) as I'd wager that's where you'll find the most progress.
Learning to lead is a good shout, get this done early - a lot of people find that leading indoors shuts them down if they don't get used to it early. You don't want to be climbing at your limit on top rope and just bumbling around on lead.
When you warm up try really concentrating on your footwork, you see a lot of indoor climbers with horrendous footwork. Warm up on easy climbs and try and make every movement perfect. The old classic of placing your foot in the right place first time is a good drill, as is trying to climb silently (no bashing around with those toes!)