I wouldn't worry too much about the shoes. I don't think they make a huge difference for a beginning climber, as long as they're not flopping off your feet. I've been climbing (purely indoors so far, outside could be different) for about a year, and I wear my shoes with socks, they're not all that tight, and I'm (finally) consistently climbing 5.10a top-rope routes.

It's possible that I will eventually hit a point where my shoes are limiting my climbing, and then I'll look at upgrading. 'Til then, though, my problem is the climber, not the gear. ;)