Veterinary technology is a good field, however in most areas techs aren't paid well and often have few to no benefits over a discount on your own pet's care. I have enjoyed the career for more than 15 yrs now and absolutely love it, but had a horrible time trying to support myself at it when I was single. You really need to look at picking and choosing your jobs if you do go this route and look for the clinics that pay better and appreciate trained technicians.
What state/country are you in? That will have a big effect on what schools you should attend. Each state in the US has it's own statutes governing veterinary technicians and you should be aware of the requirements in your state. (I can help you find your state statutes and state vet tech assoc. If you tell me what state you are in.)
You should also look at the school you are going to attend very very closely. There are lots of schools out there that offer to train you to be a veterinary technician or veterinary assistant but offer very little in the way of good instruction because they have no one that oversees their program and approves that what they teach is actually appropriate, correct or valuable. You should always look for a school that is approved by the American Veterinary Medical Association. In many states you can't sit for your boards or use the title veterinary technician without having attended an AVMA approved school.
There are a couple of AVMA approved online courses, but if you choose to take these you must be working for a veterinarian or with a registered/licensed veterinary technician who will serve as your mentor and oversee your hands-on training.
For more information on veterinary technicians and schools available, check this link: http://www.navta.net/education/index.php