This is my first post, so here goes. I hope it's not too long-winded.
I have been browsing around the forums and have found a lot of great advice that is applicable to my situation. But I still am looking for some advice on what is the best route for me.
I am just about to finish my bachelor's degree in a completely unrelated field to aviation (check that back-up plan off the list!). Once I am done, I am planning on moving to Arizona for personal reasons and I want to do my flight training there. I am pretty new and inexperienced to the field of aviation but I ultimately want to get a job as an airline pilot for one of the majors. That's the goal anyways.
So I'm wondering what is the best way for me to go. I don't need a degree, so I am fine not going to ERAU or any of the fancy, expensive schools. Since I have spent the last few years in school, I would like to get all my training, licenses, certifications, etc. as quickly as possible. I also don't want to spend a lot of money (impossible to do, I know, but whatever is the least expensive).
I am thinking of doing flight school through an accelerated program like ATP or TransPac or even ASU, etc. so that I could instruct with them to build hours afterwards. Although training with a local FBO is appealing because of the price. My question is what is the best route to get all my training as quickly and cheaply as possible (since I don't need another degree at this point) that would also put me in a good position to potentially get a job with a regional later and eventually a major airline?
So to sum it up: I don't need a degree (I will already have one), I would like to spend as little time on training (not a high priority though, I'm flexible with my time), I would like to spend as little money as I can (big priority) and I want to be in the best possible situation to be lined up with a job down the road once I have all my hours (highest priority).
Sorry for the long, detailed explanation

Any advice and/or suggestions?