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Browse credit cards from a variety of issuers to see if there's a better card for you.
There's no question that, because you have no open credit cards, it would help you a lot to have one, as long as you can keep it reporting each month with a small positive balance. (E.g. $5 - $10)
Trying to assess exactly how much it will help you is a challenge, even if you had an expert in FICO scoring sitting down with you who was carefully reviewing all three of your reports. But the good news is that you don't need that. Whether it boosts your score by 10 points or 100 points, it will certainly help it. So do it.
Choosing the best secured credit card is a different matter. I know nothing about Open Sky. I encourage you to work with people here and get lots of advice about the best choice with an aim to having no fees (monthly, annual, etc.) especially if possible.
Do you have any open installment loans? If not, there's an additional strategy we can suggest, though you should only consider it after you have improved your score with the CC.
Chat with the folks in the rebuilding forum or perhaps the CC forum and continue to get more ideas. I am not saying anything against Open Sky, since I know very little about all the options. Just important to have gotten advice from several people and to consider say three different cards with the pros and cons weighed in your mind.
Whatever you choose to do I would do it soon, so that you can obtain the scoring advantage of the card ASAP. Once you have gotten the score boost there, I would strongly consider opening a Share Secure loan with Alliant and use the full technique of paying it down. You can find out about it here. (You only need to read the first 2-3 posts in this thread.)
Having the Alliant loan in place and paid down prior to your current auto loan closing will prevent you from losing scoring points when the loan closes. I would not begin the Alliant process, however, until after you have gotten the score boost from the credit card.
Another one to look at is the Discover secured card. I think your score usually goes up with each of the first three cards you open.
Wow, really sounds like you are carefully doing your research and thinking about all the pros and cons. That's the important thing. Good luck!