Look here, I'm 27 and was in your exact same situation until two months ago. Never been in debt, so never needed credit, but realized I'd have to start building some.
I'd applied for a few credit cards throughout the years, but always been turned down (no credit history). This included my bank of over 9 years, even when I'd been maintaining a balance of over $15,000.
Here's your answer:
Capital One.
Seriously, you'll start with a $500 limit, but it's basically automatically approved (assuming you put in at least minimal income) and you can start building credit. I also got to put a sweet photo I took in Cambodia as my credit card design. My little brother started with them three years ago then started branching out, now he gets approved for all the cards with the best rewards.