Antoni,
I do not not a single pilot that has gone straight to an airline like Frontier, Spirit, or Avelo that was not an ATP graduate, not one. These airlines partner with ATP because they know the quality of the pilots produced and that the majority of them will do well in training at the airlines. Smaller schools, while potentially less expensive, typically do not offer the same quality of training and thus do not have the hiring partnerships that ATP has.
I would further encourage you to look beyond just the price quoted by any school. Many schools quote a piece based of minimum hours required but the FAA, almost nobody completes their ratings that quickly. Also, age and maintenance of the airplanes is a significant safety concern.
Check this out: Questions For Any Prospective Flight School