Some mixed thoughts about playing infantry:
1) It's a kid's game. Most go in at 17-18, buy in to the training (I don't know if you can legitimately call it "brain washing," but folks come out better disciplined then they go in, and there's something of a disconnect going on there -- my experience as a 20 year-old who was more educated and more resistant to it than most, but still refused to sleep in a sleeping bag or use anything other than the gear in my fanny pack when it was sleeting and 15^F in Germany because I thought it more worthwhile to train as I would actually perform if we had to deploy...), and play unthinking unquestioning soldiers for a few years.
If you're enough of a "thinker" that you like to get into discussions of things like "rights" and "enumerated powers," and "justice," then there's a chance you'll stand out in the ranks. In a bad way. Take it from someone who used to rag on his platoon leader for his choice of major ("hey, sir: what's the integral of a natural log?") and push the limits in general ("Sniper Check, Sir!" when saluting) -- if you stand out they can make it hurt.
2) It's a kid's game. Infantry work is painful, and IMHO the importance of the training we did was more to get you to adjust to "getting the job done" regardless of pain, more than it was to keep you in shape. Things like dropping to low-crawl (on your ear, than is) through a stream in the middle of a 6-mile run, and getting to squat on one knee for hours while waiting for orders on a night march, or 3-5 second rushes for a half mile, or playing "dead" op-for and falling on a fire-ant mound and not moving for 15 minutes while getting bit because it provided more realism (yep -- that was me).
That stuff hurts, dude. And it hurt before I got back and knee problems (I'm your age, though I am overweight). When I think back to benning and doing fireman's carries up cardiac hill, then sprinting up it, then going up it doing leapfrog in the same 10 minutes...My God but that's not for old folks.
3) You deal with a lot of stupidity. My 1st Sergeant took me aside when I was about to exit the Army, and told me about his experience getting out and reenlisting because he couldn't cut it in the civilian sector. There were a couple of folks in my unit that did the exact same thing. The advantage of the military, for some folks, is job security: polish your boots, press your BDUs, show up on-time, do what you're told, and take mail-order courses (read: copy off your roommate's courses) and you've got a 20-30 year career with good benefits.
Even if you're completely incompetent -- in this case you get a degree of power you'd never see in the real world. Those of us with an understanding of the rules and a willingness to face the threatened level of punishment from a meat-head provided we got to tell our story could generally get an a-hole to back down. Most cowed and took whatever punishments were handed out.
Just some random thoughts. It might be the perfect opportunity for you. But then, it might not...