I was in a similar situation to yours about three years ago, except I had way less 3D training under my belt. I wanted to leave my current job and dive into learning 3D. I spent a while researching schools, and based on that research decided that 3D education at public colleges was worthless (that could be wrong nowadays, dunno) and it seemed like the private colleges (art schools, Gnomon, etc) were the way to go. Except, I didn't want to be in insane debt. I figured it was up to me to teach myself for a couple years, and then reevaluate whether I wanted to enroll in a private program based on how well I was doing, how much I liked 3D, etc.
None of that ever happened. Didn't quit my job, barely learned any 3D. Long story, life got in the way. But I did learn a lot about the industry in those initial couple weeks of research. Zombie Acorn is right: you'll be paid less, work more, and be in an unstable industry. It sounds like you're drawn to the video game side of 3D, though, which is good, since it's supposed to be the mildest of the 3D specialties. Again, this is based on research I did 3 years ago, so it might be out of date, but I think with most videogame studios, you're hired on as a salaried employee, not on contract. So you get health benefits, and you don't get thrown out on your ass after a videogame ships (the way a contract worker might). In general there's way less crunch time than for 3D artists who work on movies. Less overtime, fewer weekends spent at work.
Movies and advertising are rough. You're hired on contract, maintain your own health insurance, and are basically used up and thrown out when the project is done. You're constantly spending your free time looking for your next job(s). It's possible you'll move around the country (world?) a lot. You'll work insane hours. This is especially true for 3D guys who work in advertising, because all your firm's clients will have promised their bosses they'd have something to show by, you know, yesterday. Plus, in movies especially, as a beginner, you usually don't do much actual 3D ... you do grunt work passed down to you, mostly 2D stuff like compositing and masking and crap. You pay your dues, unless you're really talented.
One drawback common to all 3D specialties is that there are very few jobs available. Insane competition. I remember looking at portfolios of people who were really talented and had been looking for work for a long time, and just thinking, "Wow, how am I ever going to survive if these guys can't get work?" You don't see that in a lot of industries, but you do see it here. Plus, a lot of work is outsourced overseas, to talented 3D mills who'll work for cheaper rates than western countries. Sometimes, even if you land a job, you'll spend time managing these overseas workers instead of doing 3D yourself. Bizarre.
But, to answer one of your earlier questions, no, you don't need to have gone through a 3D education program at a school in order to get a job. The only reasons I'd imagine people insist that you do is 1) it's probably harder to learn proper modeling, texturing, rigging, etc, on your own, away from professionals who are available for you to bug w/ incessant questions, and 2) you build connections at schools, and alumni and profs are often asked by pros if they can recommend anyone to intern or fill an open position they've got at a studio. But if you've got a really strong portfolio, can demonstrate proper technique and speed, can pick up other programs fast, and work as part of a team, I doubt you'd have your application thrown out just because you didn't have a degree. With videogames, apparently it also really helps if you've got experience as part of a team working on a fan-made mod to an existing game. A lot of guys get great experience this way.
I randomly downloaded the student version of 3DS Max 2013 today (holy cow, Autodesk gives this to you for free?!). I doubt I'll get anywhere with it, but it's fun to jump back in.
