Can you join the military with a DUI? Man, if I were 26 again and single, I'd go for being a fighter pilot or maybe a submariner. Put off the "mid-life crisis" until you're actually middle aged!
Probably. It'd have to be a pretty egregious offense with more serious attached charges to bar that.
> I'd go for being a fighter pilot
Requires a college degree, periodically requires a technical degree (that condition changes based on USAF/Navy needs).
> maybe a submariner
Be aware, this is a very isolating career field, and also broad, as there are many jobs on a submarine (or any naval vessel).
That all said, if you've got the emotional aptitude (by this I mean stability, especially if you go enlisted), it's a good way to get started or restarted. 4-5 year commitment, end up with training and a signing bonus socked away and access to funds for college. Employers also seem to have a strong preference for former military. If you find the military satisfactory you can stay in career, or go reserves (worst case is being called up for another war like Iraq/Afghanistan, normal case is a few weeks of wearing a uniform a year and collecting an extra retirement check at 60).
The message I'd like to convey to the OP is that he could have an adventure for 4-5 years, or even 10 years, and then worry about what career he wants to go into.