Beginning knitting

I am finally knitting! My grandmother taught me to crochet when I was little, but I hadn't picked up a crochet hook for years until 2005. I made a couple of scarves and got the itch to finally learn to knit. I couldn't fathom how something could be made without a hook, but I was willing to give it a try. I planned to sit down with my grandmother when I was visiting back home at Christmas, but we spent all that time talking and gathering with the whole family, so knitting never happened. Then, two weeks ago I signed up for a class at Michael's, and I am now a novice knitter and purler. This is my first project. I originally thought it would be a scarf, then I thought maybe a potholder, because I'm ready to move on to something else. This is just knitting over and over to make sure I get comfortable with it. Now I think it's time to move on to a combination of knitting and purling. But what to do with this little project? My three-year-old niece told me last night that she thought I should make a purse ... this could become a purse eventually, right? I'll post a photo when this little square of yarn gains an identity other than "my first knitting project."