About six years ago I had the same problem with bad credit working against me for jobs, get loans, etc. The only alternative was to get a secured credit card through a bank. I had to put $300 (it could be any amount) into a credit card account that would be my limit to use for purchases.
Once I showed the bank that I paid my debt on time and didn't go over the limit, they changed it to an unsecure credit card (a regular one). This happened about 2 years or less later and this was in 2011 when the economy still wasn't so great.
They increased my limit to $700. They wanted to increase it more only I decided not to. Banks try to put you into more debt for their own benefit. I still have that credit card along with others.
Watch out for offers for more credit cards when you get your credit score back up. I have had LifeLock for years and one of its benefits is you can get your credit score from all three credit bureaus each month for free. You also get your credit reports every year in one place.
I monitor my credit score through them watching it go up and down. They all don't agree with each other especially Equifax which is always a little lower and do not update their records even when you send them updated information.
I would try the secured credit card. One problem you might have is being in the military not too many banks are trusting that you will pay them back especially if you are on deployments. You might do better seeing if you can get a secured credit card through USAA.
I've never had a bank account with USAA so I don't know about secure credit cards because when I was in the army, they didn't have all the services they have now and no internet so you know that was a long time ago.
When I was enlisted in the army, I was always broke especially from overspending. It's very easy to get caught up in and I even got into trouble with my bank for overdrawing my account. That can also cause disciplinary problems from the military as well. Fortunately my situation wasn't so bad, but I knew others that got into a lot of trouble for huge debts.
I forgot to add: Your credit score is actually better than mine was in 2008. Mine was zero. I never heard of that happening before so I guess I'm fortunate to get mine back up into the upper 700's.
The Financial Improvement Team (FIT) helps members with Debt Management, budgeting and building and maintaining good credit. If you would like to speak to this team, please call (800) 245-9360 between the hours of 8am-6pm central time. Best of luck!