Inconceivable said it right up above. Local mom and pop would be the way to go starting out. They would probably even be the way to go in the long run if you think about making it a career.
I would stay local for your private and instrument. If from there you think this is what you want to do. Then go commercial and CFI at one of the bigger establishments if the wallet can afford it.
Based on my experience no one has every asked me where I learned to fly. They simply want to see total time requirements and that you can fly.