i went from squares to a hat.
I like to jump into things but not too much!! (so a sweater or socks would have terrified my but a hat was ok)
I picked a hat which would teach me a couple of new techniques but not to many so that i could get my head around it. The hat patterni chose was worked in the round (teaching me circular knitting on DPNs) and had two types of decreases. I was so proud of myself and felt so cool for using DPNs.
I think the best way of choosing a newproject when you are learning, is to find something which is 75-90% things you know ad 25-10% things you dont know and can learn on the job. so if you can do knit and purl stitches but have never tried ribbing or decreases or increses a ribbed scarf with eyelets (created using simple increses and decreses) would be interesting, or a washcloth using ribs and pearls to create a picture could also work.