I'd say first take a look at your bank's or credit union's website. If they offer you a good card, I'd stick with them (If you've been pleased with their service thus far).
With your scores you'll almost certainly qualify for a no annual fee rewards card. You might not get approved for some of the higher-end cards due to your short credit history, but that'll come with time.
Here are some suggestions:
If you or a family member are or have been in the military
Navy Federal Credit Union nRewards Visa card. They have a card with no annual fee, a simple 1% back rewards program, tend to give great credit limits and have excellent customer service.
Also the Pentagon FCU Platinum Visa card has great rewards. 5% back on gas and 2% back on groceries each month with 1.25% back on everything else.
Credit unions in general have lower interest rates on credit cards, so if you're a member or are eligible for membership, take a look.
If you are a Costco member
The American Express True Earnings card has no annual fee if you are a Costco member, has some of the best rewards out there (3% on gas, 3% back on restaurants, 2% back on travel and 1% back on everything else). AmEx also is also great with warranties. Buy a laptop and it breaks or stops working? Give them a call and there's a good chance they'll cover it.
If you are a Sam's Club member
Don't know much about this card, but the Sam's Club Discover card is highly comparable to the AmEx True Earnings.
Otherwise
Bank of America and Citibank both have a wide selection of cards including rewards cards. My favorite from Citibank is the Dividend Platinum Select Mastercard and my favorite from Bank of American is the Cash Rewards Platinum Plus Mastercard.