You don't need J1 for flight training that is for the purpose of being trained only.
All you need is M1 visa as long as the school can issue I-20 form which you need for application for M1 visa. J1's going down fairly soon, but that DOES NOT mean M1 visa will be scraped. Imagine the problems for US companies dependent on students on M1 visas. Anyway, M1 could be issued up to 12 months and extended again for another 12 months if you're thinking of time.
So, whether you have some flight experience or not, as long as you don't need to work as an instructor in the USA (main reason J1s are popular, especially in rotary world) for the rest of the 2yr period, you should be just fine.
ACF didn't have M1 options in the past, but I've read on PPRuNe that they're sorting it. So it should be fine. I bet you'd change your mind as to which school to go to, many times over.
Whether smaller or bigger school, Florida, Texas, California etc, it's all up to you.
Check out the threads on flight training in the USA and visa issues if you need more detailed info. What I wrote pretty much covers your fears and shows it's no prob.
Yeah, I'd be interested to see if there's 'replacement' visa category/class in the making as I've read in one newsletter from one US flight school (that's what US govt presumably put into ether). Otherwise playing around with F1 visas doing college or Uni degree etc. I won't have the rest of my funds (slaving away) anytime soon and don't have time right now anyway..