I started out with a similar amount of money (about $2,000) and put most of it into one company, with a view to simply buying something I thought would go up in the short term (weeks) and sell. It was as much about just going through the process of buying and selling something to learn how it works as it was about making a bit of money (I think I sold out a few weeks later for a $200 or so profit, so my learning experience was a pleasant one). I made a few similar trades just to get the hang of it all, and was lucky enough for all of the first few to be profitable, often amazingly so (proportionate to the amount invested - often 20-40% within a week, although with such a small amount of money it wasn't a case of massive profits). It could just as easily have gone the other way, so keep that in mind. If you're a 'hands on' person, doing what I did will teach you more than reading books. Most people feel more comfortable reading books and arming themselves with a lot of theory, but for someone like me that would have been counterproductive as I'd have trouble mixing my theory with my practice.
If you're really keen to get into stock trading, jump in and go for it, knowing you might lose some money, but also knowing you'll quickly learn a lot. I would never have taken the theory as seriously if I didn't have real money on the line.
If you just want to find a nice place to invest some money and leave it sitting there without having to think about it too much, it's probably best to wait until you have more money and a strong reason to think a particular stock is going to go up. From a practical point of view, $1,500 isn't really worth putting into the stock market and these days I wouldn't make a trade of under about $4-5k, but $1,500 is enough to buy something and see how it all works, without it being more than you can afford to lose (well, I'm assuming). If losing $500 is going to be a big problem for you, keep your $1,500 in the bank. Right now is a particularly risky time to be jumping in for your first experience.