When I was a college student, I was flooded with offers. They covered campus (mailboxes, student newspapers, booths giving free gifts, bullitin boards, etc). You should be able to get any of them. Credit card companies try really hard to get college students hooked on a CC. Find one that looks good and you shouldn't have trouble getting it.
There are a few things to look out for.
(1) Pay in full each month. If you won't do it, don't get a CC. Leave and don't come back to this thread.
(2) Ok you are still here, you will pay in full. Interest rates thus mean nothing.
(3) Pay attention to perks (don't get airline miles if you never fly), annual fees (you don't want a card with one), and grace periods (how soon after the bill is printed do you have to pay it).
Basically this first card might not be the best (low limit, lower perks), but it'll build your credit so you can get a great one in the future.
Once you get a CC, it is far better than a debit card. A CC has many more federal consumer protections, a CC generally gives much better perks, a CC gives you interest free loans, a CC purchase builds your credit when a debit purchase doesn't (saving you thousands in your lifetime), a CC purchase costs less to the store thereby keeping prices lower, etc.
