Man, I don't envy the load you're about to undertake. Becoming a CFI has a LOT more involved than flying around learning to teach people. It is a bear, and the most commonly failed checkride in the USA. It think it's like a 75% fail rate.

Not only is it a lot of money and flying, but the biggest load is the studying and memorizing the Fundamentals of Instruction (FOM) stuff. The FOM test is a joke, but the FOM stuff you must know for the checkride is a lot and it's BORING.
Plus the gigantic CFI notebook that most candidates need to compile is a pain too. Mine was about 500 pages long of work I had to research, type, and transcribe.

If all that didn't change your mind, then you probably have what it takes to juggle being a CFI and another job. I would suggest going down to your local FBO, one with nice, new airplanes, not the old beat up ones you find in most Florida flight schools (those are better for time builders headed toward the regionals). Learn from them, and before you pay any money, ask them if they will hire you once you get your CFI (given your unique schedule and situation). Many flight schools think they can make their CFI's do anything and will expect you to be available from 4am to midnight 6 days a week.

If you really want to instruct on the side, you'll definitely want somewhere close to where you live/work so you don't have to drive 45 minutes each way to get there. Also you'll want nice, new, comfortable, well-maintained planes to fly since you might be there for a few years. The fun stuff wears off after about 6 months, then it becomes a job and you'll want to feel safe and comfortable doing that job. The new planes will cost a little more than the old ones, but they'll still be cheaper than going through one of the academy or university programs.

Make sure the school as a high percentage of newer planes too, not just one or two with 5 planes from the 1970's. You'll probably be stuck flying the older ones 90% of the time since the career oriented students want to save money on their flight training.