Do something reserve. Personally, I would go Army National Guard as my first choice but Army Reserves would be okay as a second choice.
The part timers (reservists/guard) go through the same basic and AIT training as the regular military. The difference is that you get to go back home while everyone else gets shipped off to their new unit at the end of training. I'm not completely sure about this, but I believe that it's easy for you to move from part timer to full timer (regular military) but not so easy the other way around. Your one weekend a month and two weeks per year is usually laid back and easy but it can also be an interesting break from your normal work. So, when all your training is over, you can reflect and think about your options. If you really enjoy the military, you can turn full timer. If you hate it or if you are content with part time, then you can continue that track.
Now that you have decided to go the part time route, consider that you will be limited in job by the area that you decide to live in. If you are willing / able to live anywhere, then you may want to relocate to the area where you can get the best job. For example, I served with an Army Reserve Chinook unit out of Ft. Lewis in Washington. The unit was amazing. We could hop on Chinook flights which were assisting the state in the national parks. The unit was active, had great funding and there were several full time opportunities for me right at that unit (full time reservist.) Another aviation unit (National Guard) I served in was a Blackhawk unit which was poorly funded. Many of the Blackhawks were grounded and we got few opportunities to fly on them.
I would research the different jobs in the military, compile a list of the jobs I might want to take and then do research to find out where those jobs might be available. Some of those jobs are limited to certain units (aviation). Other jobs are available at any unit (supply). I would also consider where I would like to live. I believe that National Guard units can be just about anywhere because they are state while reserve units tend to be on the same bases as the regular military. If at all possible, I would try to contact people in these different units to find out what sort of help they really need and what the unit is like. The openings you will get presented with when doing your job selection don't always match the most critical needs. Also, the unit might have full time work available for you if you choose a certain job. Finally, I would try to visit some of the locations on my list.
An additional benefit of being a part timer is that you can get a lot of help with school through various tuition assistance programs such as the GI Bill. You could be nicely setup between part time work, your one weekend a month, tuition assistance and full time school. Your unit might even be able to set you up with cheap housing on base.Of course, you would need to make sure to select a unit with a location close to the school you would want to attend.
For school, I believe that National Guard provides even better benefits. I believe that on top of the GI Bill, you can get your tuition fully paid at a state school. Just make sure that if you go the National Guard route, that your unit is decent and gets decent funding.
I ended up moving around and making a bunch of stupid mistakes. If I could redo my time in the Military, I would have stuck with the Chinook unit out of Ft Lewis. The unit was awesome, in a beautiful location and next to a great school (University of Washington) I could have had my choice of a few different full time job openings for decent money. With tuition assistance, a free place to live on base, meals served and a cushy job I could have done really well. The problem was that I had no idea what I was doing or how the system worked. The recruiters were worthless in that regard. They only want to get you signed up. Be very careful with the recruiters and don't let them sign you up for anything until you have fully figured everything out on your own. I would still talk to them to see what help they might be able to provide in contacting units though.
I don't know much about reserve units in the other branches, but I imagine they are a lot more limited in choice compared to the Army. Of all the branches, I believe the Airforce generally has the best facilities. The branch is a bit more recent and they get great funding. You can go through the same process with these other branches though.
Make sure that you get a good ASVAB score before looking to join. A good ASVAB score will determine what job you can get. I was able to get pretty much anything and aviation requires a relatively high ASVAB. People who do terrible on that test get stuck in shit jobs.
Personally, I would stay away from anything infantry and other "boots on the ground" jobs. Stay away from truck driving and crap jobs like chef. I did some motorpool duty and found it to be horribly boring. Pick an interesting job which won't put you in the middle of combat. That said, a lot of the Chinook jobs actually are considered combat because if you have to ride with the Chinook, then you might be going into some hot areas.