Welding is hard work and can be hazardous to your health. You will be working in small spaces or maybe at height, and you will get burned by molten sparks and have to breathe in poisonous fumes.
If you take a welding job at a factory or in an automotive field, you will be lucky to make better than minimum wage. But, if your good enough and have enough grit you can work your way into a very well paying job. Welding is skill based, so if your not good at it you should never expect to make any money doing it, the best paying jobs are for those specializing in micro-tig, rare alloys or high pressure pipe. The first 5 years of your career will be spent learning, but mostly your just going to be someone elses under paid *****. Once you have some experience, get some tickets and are a journeyman, the doors and opportunites will open up. I like welding, but alot of people probably couldn't hack it.
I can't help you with schools, in Canada everything is standardized under the government and the CWB(canadian welding bureau). A CWB ticket is good anywhere in canada, but from what ive been told just about every state, city and region in the US has its own regulations and tickets.