Everyone's thrown out good questions so I don't really have much to add, but if you've never had a credit card what types of scores are those/where did you get them? Are they vantage scores from credit karma and the like or are they actual FICOs? I ask because if you can't generate a fico score yet (you need 6 months of recent reporting from some sort of loan, be it a credit or charge card or an installment loan of some kind - auto, mortgage, student loan, etc - collections alone will not generate a fico score) you might be better off starting out with a secured card.
Personally I'd recommend the discover secured card hands down over everything else, the cash back is pretty much unparalleled among secured cards (not to mention it's doubled the first year), they'll start reviewing your account to graduate to unsecured and return your deposit starting at 7 months, and personally I think their customer service is top notch. If putting down $200 bucks up front is a little much for you you could also try the capital one secured MC, you could be eligible to only put down $99 or $49 instead of the full $200 - or you could even get both cards, that's what I did and I'm really happy with both. Either of those will save you a ton of money in the long run over going with first progress or credit one or the like on an unsecured card that won't require that refundable deposit but will charge you a nice fat nonrefundable annual fee, most likely with some other random charges thrown in for fun.
Also before you do anything I'd suggest you try out capital one's prequal tool, they have a few cards for limited/fair credit so you might not even need a secured card if you get a hit for platinum, my SO got a platinum from them with no fico score, and not that long ago, so it's definitely possible.
However you proceed I wish you luck, I'm sure all the smart folks on here will be able to help you out with what to do next, my advice is only based on my limited knowledge lol I'm sure much more experienced people will be able to help you a lot more but whatever you do I know you'll get to where you want eventually!
