Should I be worried about planning on being an OTS hire?

I am in high school and would like to eventually go to the airlines. I have access to an airplane and am planning on doing the rest of my ratings in it with a freelance instructor (I already have my PPL). I plan on CFIing at a local "mom and pop" school where I have connections, but recently I have been seeing that airlines are just hiring their cadets and not people off the street. Should I go to a part 141 school so that I can get in a cadet program, or stick with my current plan?