I've worked in the field of computer animation for over 20 years, getting my first Hollywood feature film visual effects job in 1996. I've worked at some of the highest-end Los-Angeles visual effects shops in supervisory roles and also in hiring manager roles. I've worked in feature film visual effects for 17 years and in the computer game industry for the last three. It's been a lot of fun but it can also be hard work. Here are some quick thoughts:
*I'd recommend avoiding pricey schools. There are people in this industry who have no formal education and others who have spent a ton of money. Certification means very little in this industry: it's chiefly all about your demo reel: can you animate/texture/light/rig/comp? That's what we care about, not where you went to school. There are plenty of self-taught people out there and the software and hardware is fairly cheap. I'd recommend getting student/demo cuts of software and teaching yourself at home to see if you enjoy it and are good at it. I know guys who spent tons of money and are still paying off their student loans in their 40's. Don't be that guy. That guy is sitting right next to some other guy who didn't spend much at all.
*The most successful people in this field are both artistic and technical. Makes sense since you're creating art on a computer. You don't have to be a genius at both but you have to be some sort of artistic problem solver. People who are pure artists tend to run into mental roadblocks when they need to debug a render that's not working and purely technical people aren't going to be able to create art. That's not to say that there's no place for these types of people: pure artists tend to do things more like concept painting while purely technical people do more of the programming, but if you want to be an animator, lighter, texture painter, fx artist, or rigger, you're planted firmly in the artistic/technical divide.
*Most of the feature film visual effects industry has undergone a pretty big upheaval in recent years, with much of it moving out of the country to follow tax incentives. Digital Domain and Rhythm and Hues declared bankruptcy in 2013, Dreamworks had markedly decreased its staff, and Sony Imageworks has moved most of its people to Vancouver. Quite a lot of the feature film visual effects industry is in Vancouver now. Pixar, Disney, and Industrial Light and Magic have so far been pretty stable, though ILM also has a satellite facility in Vancouver now.
*Most feature film visual effects work these days is freelance, and this is doubly so for entry level people. A typical first few years (or more) in the visual effects industry is spent hopping around from shop to shop as you start and complete projects. When you're young and unattached this can be fun: work in Vancouver at Sony Imageworks for one show, work in London at MPC or Double Negative for the next, then jet down to Wellington New Zealand to work at Weta for another show.
*You won't have much job security of you define job security as working at a single place of employment or in a single geography. Visual effects is a commodity industry, margins are low, and many are run by non-business people. Shops go bust with alarming frequency and even if they don't, as a project hire you're probably going to have to look for new work the end of the project. That said, people with good skills seem to always have work, though they may have to move around to stay employed. If you're the type who wants to buy a house and settle down, this probably isn't the field for you, though as you gain more experience you might be able to land a staff job somewhere.
*The game industry at a top tier place (Activision Blizzard, Electronic Arts, Take Two Interactive, Riot) seems to be more stable than feature film visual effects and that's where I am now. Successful game companies own their own content and can charge a premium for it (i.e. they are NOT a commodity industry), leading to healthier profit margins and balance sheets. That's not to say problems can't occur. All of these mega-successful companies are hit-driven, where the lion's share of the revenue is made by one or two games. When that game fall out of popularity, something better be in the wings to take its place.
*Hours can be tough. 80+ hour weeks can be common. During a push to get a film trailer out or to deliver a show 100+ hour weeks can happen. This didn't bother me when I was younger because I loved what I did and I was surrounded by a bunch of other people who loved what they did and were super passionate about it. It can be harder when you're older though and you have a family or hobbies you want to get back to. The long hours are more prevalent in visual effects than at game companies but it can happen in game companies too. Generally (though not always) the bigger game companies seem to have more normal hours since they're able to hire more infrastructure. I have it lucky now working at a successful game company and the hours are great, more around 40-50 hours a week. When working on movies, CG features tended to be more sane than visual effects shows since you can mass produce more easily on a CG animation show: each shot is much more like the surrounding shots than with a visual effects show, where more stuff has to be hand-crafted per shot.
Mike