Alec, I had kind of similiar situation when I was 19 -- nowhere job, no prospects for the future. My family was supportive, but I saw that my future wasn't going to be what I hoped for. So I went down to the recruiting office to join the Navy -- my grandfather served in WWII on a destroyer and always talked positively of his service. The Navy recruiter rubbed me wrong though, so long story short, I dropped out of community college and joined the Marines for what I originally intended to be a 4-year tour. I wanted to get my head on straight, do something I couldn't do anywhere else (I joined the Infantry), and generally get away from my situation that didn't feel had opportunity for the future I wanted, however vague those ideas were. That was in '87. I retired in '08. I stayed in for various reasons. One was that I still didn't see any real prospects on the civilian side. Another was that I didn't get any college done during my first tour like I wanted to (I spent much of my first four years in Okinawa deploying all over the pacific, and generally having a good time), and most importantly, I enjoyed what I did and the people I was with. That's not to say that there weren't days that life sucked -- poor leadership (which is found everywhere), and the life of an infantryman often involves being dirty, cold, wet and tired; but I still enjoyed it immensely on balance. So I re-enlisted with the intent to finish up a bachelors degree and move on. I found that I enjoyed my second enlistment as much as my first. I was able to finish a bachelors degree (online) using my benefits, and met my wife. Of course I deployed, and did the things associated with the Marine infantry. I found myself in positions of leadership (somewhere I never expected to be), and was greatly rewarded in those positions, mainly through mentoring younger Marines, and seeing them become successful in the military, and later in civilian life. After a couple of tours in Iraq, I decided it was time to retire (I did 21 years and change) to be with my kids before they were still in the house. The combination of my education and experience landed my a job with the Army here in Wisconsin. I did a tour as a drug/alcohol counselor while on active duty (the Marines used to take senior NCO's and train them as counselors-I did that for 3 years)--I do something similar with the Army now, but in a supervisory position. I'm also working on an MBA with my post 9/11 GI Bill - I retired before we were able to transfer it to family members, so it's use or lose for me.
The biggest thing I got from military service was options. Once I was ready to move on, I was able to pick and choose where I went next and what I wanted to do. I learned leadership and generally developed things in me that I didn't know I had. Also, being retired from active-duty gives me a monthly check. It's not much, but it pays the mortgage, and gives me options on what employment to take - I can walk from this job anytime and still have something coming in. I've also got a variety of skills that I can use to gain employment -- infantry skills can translate to security contracting (I got offered jobs from a couple of security/training contractors overseas), drug/alcohol, and sales from my tour as a recruiter. But it's more than that-I gained so much experience in life and had the opportunity to see and do things I would have never seen otherwise: I did reconaissance and interdiction in the SW United States, patrolled the jungle in the Phillipines against guys out to do us harm, cleared houses in desert villages in Iraq, coordinated food/medical in refugee camps in Indonesia and Iraq, and yes, went face to face with people who had my death as their primary goal, but honestly, I did far more humanitarian than combat missions in my career. I also made friends that are closer to me than my family, drank beer in over 25 countries, and looked damn good in uniform. I wouldn't trade the experience for anything.
As an aside, since 2003, everyone joining the military, especially the Army and Marines (not to discount what the Air Force and Navy do) know what's in store for them. I've never seen a group so willing to serve despite the known risk. When I joined, the Cold War was on, and I joined to fight the Russians (imagine my surprise when we went to Kuwait instead of the Fulda Gap), but there wasn't any shooting going on. I don't know if I would have been so willing to raise my hand if the situation was as it is now. For that reason, and people like you, I have enormous respect for anyone willing to serve today.
You're joining an elite club-a tiny percentage of the population currently serves, and it's a brotherhood that will remain long after you've hung up the uniform.
The only advice I would give is whatever your MOS, and whatever job you happen to be doing, do it to the best of your ability, and never turn down an opportunity to gain a new experience.