Hey there,
I did the same thing 9 years ago. My advice would be to avoid flight schools that are in or near very busy airports. I did my conversion from a CPL to a ATPL at Boeing Field in Seattle. The amount of radio chatter was something that took some getting used to. Things are done a little differently here, at least from what I was accustomed to. The controllers can lose patience quickly if they are swamped so it can add unnecessary pressure.
The regional airline outlook is quite good, with lots hiring. Unfortunately, there are a lot of pilots with lots of experience trying to work a foot in the door at the larger airlines, so competition is quite intense, and several airlines won't look at you unless you were referred. So it really depends what position on the field you are looking for.
Also, another obstacle I faced was that a very large percentage of the pilots here have a degree (doesn't really matter what it's in) and most airlines look for at least 2 years of college. When I was flying in Oz, almost none of the pilots I new had college degrees. It wasn't common. So, in order to be competitive here, you might need to do some more school if you don't have any beyond year 12.
Here is one site you can check out if you haven't seen it. It'll give you an idea.
www.atpflightschool.com Also, Air. Inc, as previously mentioned can help.
Expect to go through the wringer to train and fly here because of the increased security, especially with foreigners learning to fly. Even after flying with the same airline for 6 years, when they sent me to Airbus training in Miami recently, I had to get fingerprinted....again, back-ground checks....again, along with a bunch of other hoops to leap through (many of which I had been through after Sept. 11). Just thought you should know.
www.flightschoolcandidates.gov/ Hope that helps, and let me know if I can help in any way.