Good that you want to start investing when you are young. Bad that you are already in debt up to your eyes. I first recommend paying off as much of your student loans as possible now. But if you can't or just want to invest now, that is not an awful decision as the interest on student loands is tax deductible and therefore does not hurt as much as the interest on a regular loan. Someone here said pay your debts first, always. I disagree. Pay your debts off at a reasonable rate, but if you can earn more money by putting your money to work than the interest rate on the loan, there is no need to pay off a debt to the exclusion of investing.
Anyways, back to the topic at hand. Because you do not have much money and will not for quite some time, stocks are not a good option for you. Because you have so little cash to spare, you will only be able to buy a minimal amount of stock per transaction. Each stock transaction costs a fixed dollar amount, e.g., 7-21 dollars. If you are buying 50 bucks worht of stopck at a time, you need at least a 20% return on that money just to break even. Not a good idea.
A better option would be to find a low initial investment mutual fund that allows periodic, no fee automatic investments. Vanguard offers a number of these funds. I'd go with some kind of index fund. It doesn't matter which one per se, so long as it is composed of a wide variety of highly traded stocks (i.e. companies you know, Samsung, Best Buy, Intel, Target, Microsoft, etc. etc.). Budget a fixed amount that you can afford to deposit in this fund on a periodic basis, i.e., every two weeks. It doesn't matter how small (although some funds have minimum reinvestment amounts). I started with $50 biweekly investments at 23. As I have earned more money, I periodically allocated more for my investments. I am now 30 and invest about ~4k a month into 5 different mutual funds, with over $100k accrued ($86k principal, $14k in capital gains).
If you are really really strapped for cash or cannot find a mutual fund with a low enough initial investment, start with CD from your local bank. Most banks have programs where you can allocate a certain amount of money towards the purchase of a CD each week. Once you have enough to invest in a mutual fund and can convert the CD, do it and invest in mutual funds as indicated above.
No matter what anyone tells you, investing in individual stocks is very risky. Unless you are very familiar with a company and do not mind the idea of losing your entire investment, do not invest in individual stocks. that said, higher risk = higher potential reward, but at least make an informed decision. But if you have to invest in an individual stcok now, take a look at Chemed and Apple. Chemed runs Roto Rooter and a hospice insurance company, and is doing quite well now. Apple is way up right now and so is probably not a great buy, but if you follow macrumors and time our investments before the announcement of new products (e.g., January macworld), you can do quite well, I know I did last year.
Good luck!