The local school would probably be fine for most of the ratings. Some schools don't have a twin and the CFI is best done somewhere than does a lot of CFI's.

The airlines don't care where you train. It's about ratings, experience, and background. Yeah, some big schools have RJ courses and hiring "deals" with the regionals but these things are carrots to get you to pay more to train there. These things CAN get you hired faster but at what cost? You could instruct a while longer and build up your experience to where you don't need any "deals" to get a job.

It's up to you.