Either your recruiter is a shitbag, or he's met his quota and doesn't give a shit. Maybe both.
Yes, the AF is more stringent on that type of thing. they have all kinds of controls in place to try to bring in higher quality people. i don't mean any offense by that, just a fact of life. Between a guy with zero record and a guy with a record, who would you rather hire without knowing more facts?
A couple of options;
Find another AF recruiter nearby. Even if he can't bring you in, he might be able to advise you better than this shitbag. He may actually be able to take you in though. Worth a shot.
I don't know how recruiting cycles work, but if you can find out when one ends and another begins, he may be hurting for people and he may pay you more attention.
Tell the shitbag you're talking to the Army. Sometimes that'll motivate them to get off their fat, lazy overpaid asses and do their job.
When it comes to jobs, they handle that at the MEPS. After a full day of complete ass-hattery, anal probes, blood tests and other stupidity, they'll take you into a section where they expect to feed you into the system and shit you whatever job pops up. Yah! I get to pass out towels at the gym!
Don't take it. You can seek vocational areas, like mechanical, admin, medical and general. Not ideal, but if you have no training, no skills and no exact job in mind, it can help.
Otherwise, tell them you'll come back another day to try the job market. they won't want to hear that, but oh well. Jobs are spit out constantly.
There are some constant jobs; CCT, PJ, i'm sure the cops are always hiring, and so on. Ask about those jobs.
If they offer you a job, ask others about it. Don't just read their cookie cutter desecription of the job. Ask people who know and give a shit. Some jobs that sound great really aren't. Some of those jobs have a big recruiting bonus for a reason! nobody wants them!
Keep us informed how it goes. One concern i have for you guys is being husband and wife (I assume), going in together. I knew a guy who worked on the B-2 bomber. His wife worked on the F-15. There's only one base in the world those two could ever be stationed together, and that's Edwards California. That can get rough. It may take some sacrifice on someone's part. one of you may take the "Cool job", being a PJ, while the other may have to take the common job, like admin, medical, etc.