Since it is your first card, you'll probably be limited in what you can apply for (since your score is probably just getting established).
Find one that doesn't have a too high of an interest rate (they all tend to suck) and make a personal plan to try to not carry a balance. In other words, make sure that you can pay it off monthly. That will help to establish and improve your rating and hopefully you can avoid the trap of too large a balance, high rates and only being capable of making the minimum payment.
Once you've got a reputation for paying on time, other cards with better rates and/or rewards will start approaching you.
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I know I won't have any problems paying on time, right now I only plan on using it for small online purchases. And what is the process of applying? Do I just walk into the bank and tell them i'd like to apply for a credit card? And what types of questions will they ask me?
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You can go for a card from your bank. If they have accounts of yours and you have a history with them, that may be a shot at getting a good interest rate. If you are capable and willing to pay it off monthly (and carry no balance) then an interest rate may not be too big of a concern. http://credit.about.com/od/credit101/tp/beginner-credit-tips.htm That link has some good advice and things to consider.
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Okay i'll read the article, thank you.