Going to start building up my credit rating

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I am a 21 year old junior in college who doesn't really have many bills so never saw the need for a credit card. I have had 1 credit card in the past, but due to the ease of my debit card I rarely used it.

Now im ready to stop using my debit card and I wanna find a credit card that wont cost me a penny to use (are there even any cards out there like this?) so I can build up my credit rating.

What card should I get? I plan on always paying my bills on time and I am very good with budgets/money.