I just started too. But my first project is a scarf so that doesn't help you too much.
My friend who taught me said that a hat isn't too complicated for a first project either. I'm pretty sure hats are usually knit in the round, but so is my scarf and I've been fine with it.
Years ago when I first tried to learn, the friend who was teaching me was trying to get me to knit a dishcloth. It makes sense--it's not complicated and it's fairly small--but it didn't hold my interest and I abandoned it. So make sure to choose something that will keep you motivated and wanting to work on it.