I'm not a fan of the ACPP program at ATP, as you get all you go from PPL to CFI in 90 days and then turn around start teaching. Your local flight school maybe be just as good of a place to get your ratings through Commercial, then an ATP type of school for a rating or two. You can save a lot of money doing it this way and end up with better training, in some circumstances.

Flight training is 90 percent about you (attitude/desire), your CFI (experience), and an airplane (balance between cost/quality).

I wouldn't worry about "connections with quality airlines". If you put in your time to become a good pilot, you'll have the experience to get hired. In this day and age, connections are highly overrated.