CFI jobs
Congratulations for deciding to take the plunge. Lots of luck, too. Read some of my posts for a cautionary viewpoint.
No, you shouldn't have necessarily signed up with FlightSafety's ASA program a year ago, P-F-T notwithstanding. They gave you a good sales job. You should still apply to FSI as a flight instructor. It never hurts to put your resume on file.
For that matter, send to every major school, commercial, college, whatever, on the planet. Your chances improve with the more stuff you send. I've been there; I've done it; I know.
I can tell you that life at a major school has its pros and cons. Pros include, obviously, flying and building time, but also making contacts. Depending on the school, good facilities and advancement opportunties. I worked at two big schools, Riddle and FSI. Both places had good equipment. Also, a lot of mickeymouse. Pay will vary. In retrospect, Riddle paid very fairly; FSI, somewhat less than fairly. Both places had good benies. I can guarantee that I could substitute Pan Am for either name and it would be the same.
Try looking in pilot magazines for names of schools and send stuff to them. My rationale was that these schools might need instructors. It worked twice for me; I got jobs at FSI and Mesa after seeing their ads, and I learned about ATCA in Goodyear after seeing them mentioned in a Beech ad. I had an interview at ATCA.
Good luck with your job search.