You can brew any style you want- but you may not want to do a barley wine or an oaked beer that takes a long time to age!
What commercial beers do you like? If you like Sierra Nevada Pale Ale, you could very easily do an APA that would be similar in body and taste. If you like hefeweizens, make a hefeweizen!
Most beers can be made with extract only, extract with steeping grains, or all-grain, so you can pick just about any style you want. I'd stay away from lagers, though, if you don't have a way for precise temperature control and the patience of a saint. Otherwise, you can make whatever you'd like.
If you're a beginner, sometimes it's easiest to purchase a kit, where the ingredients are already put together for you, along with good instructions. I really like the kits at austinhomebrew.com, and their website is great. It has the styles of beer, the commercial clone kits, and reviews on them right on the website. They have very good instructions, too!