What should I study to help get a job working for a three letter agency?

PFC (Join to see)

Yes, of course you should be prepared (study) for any position you are looking at moving in to. I hope you took the time to learn what you were looking at joining the military? IF you are using military experience to get into one of those 'three letter agency' than that was a smart move BUT you also need to be pursuing civilian education too. Much of what education depends upon which agency you are looking at too?

Complete your degree -- Not only STEM and Computer Science degrees for NSA, but also regional degrees, ie. Asian Studies, Latin American studies, African etc. But there are also non-technical/ non-math jobs at No Such Agency -- Main thing get your degree.

Obtain and sustain your clearance, the higher the better.

Make yourself competitive in the job force through experience, education and clearance

Be mindful that you're going to need (although in your Army job you probably already have) a high-level security clearance. That means, mind your p's and q's when it comes to things like debt (of any kind, even credit cards), things you put out on social media, and who you associate with (ie if you have friends that are crooks, distance yourself.) If you are gay (no need to confirm or deny to me here), make sure you disclose that, or anything of the sort that people typically hide from families and loved ones. If they see you're trying to hide it, it becomes blackmail fodder. Common sense stuff, really.