I second apping for two together. The inquiry hit is much less than a new account hit and a new account takes about 1-2 months to show up on your report. Plus the inquiry only hits 1 out 3 reports (unless you app for a Capital One), but a new account hits all three together. If you know which bureau is going to be pulled, you can spread out your two apps.
With your score, I will start considering a prime card (Chase, Discover, AMEX, BoA), Perhaps a cashback card of your choosing. One recommendation though, make sure you credit card statement closes below 10% balances before you app. You don't have to spend less than 10% than month, but pay it down to that before the statement cuts. This should put you in the best chance of being approved.
Consider a AMEX revolving product as the the Blue Cash Everyday (or Preferred, if you spend a lot on grocery monthly). While most prime credit cards I have dealt with seem to grant credit lines that are in line with my current ones (espesically true if it was my first card at the credit card company), my AMEX revolver grew the fastest because the generorus 3x CLI after 60 days and 6 months. With your income, you can easily grow it into 10k+ within two years. One draw back is that I think it is relatively harder to get approved for.
I was in similar situation as you are two years ago. Oldest card was 2.5 year, another just shy of 2. TransUnion and Equifax were ~750. Got my util down to 10% and I apped for Amex BCE, Citi Dividend and Chase Freedom all within the same month and got approved for all three. So I think you stand a fair chance to do two prime cards at once.
Obviously if you are having a major credit activity (e.g buying a house) within a year or so, I'd hold off apping until you get that out of the way.
