Find a strong pipefitter/steamfitter union in your area. Do some research and see what it takes to get organized in. Work hard and move through the apprenticeship program. There you will actually learn how to fit as well as weld, kinda important.
Is welding a good career?
Well if you don't mind working hard, getting dirty and going anywhere the work is, it pays pretty darn well IF you are good at it. There is definitely a shortage of welders in this country. Not enough good ones to go around with all the different construction jobs going on, and it's across the trades; fitters, ironworkers, boilermakers.
From one of my favorite celebrities: http://mikerowe.com/2015/11/rubioweldersphilosophers/There’s nothing magical about learning a skill or earning a degree. What matters most is the same stuff that’s always mattered. A willingness to work hard, to master a skill that’s in demand, and to go where the demand is. Work is not about the color of collars, or the relative size of the paycheck. It’s about pursuing opportunities where they exist, and creating them where they don’t.