So many responses! Thank you all so much for taking the time to reply.

Obviously I can't go sign up for five credit cards. Student loans incoming! But is it a bad idea to sign up for one card? I'm not sure if they would accept my application or not, but I have had a couple of offers sent to me.

I do have a debit card. Can you get a points card through any bank or would I need to change banks?

Also, I tried to check my credit score and nothing came up, but I have been making payments on a car for a year. Shouldn't that count for something?