Well, to be honest, no brand new CFI has a "good gig" right away. Those pilot mills have you do the call center the first then you get asigned to a location somewhere.
I cant promise anything, but chances are you would have CFI gig at the end at Wisc Av, but its up to you to get students (hours) kind of. From the few years I spent there, most guys who went all the way through to the CFI had that option for them at the end. Its not like a pilot mill where they have a marketing department set purely on finding students. They do of course to some extent, but keep in mind its a local FBO, that sells hangars, fuel, charter and stuff as well, and its not a nationwide network of schools. Of course there are some walk ins like yourself that are dead set on flight training, but you also do introductory flights and sell it. maybe 1 of 5 or 10 who came in to learn about flying because they arent entirely sure if they want a license actually end up doing it. But the art is really in selling it to them on the intro flight. Dont make it complicated, show them how "easy" and "rewarding" your "investment in flight training is". <- useful words to use on a would be pilot.
Took me 4 months to fly about 10-20 hours a week with regular clients, some weeks pushed 30 but you know that wisconsin weather.... But some other CFI's had a full schedule right away. Its part luck part skill. I was there during the bad economic times of the past 5 years or so. So i had less than average hours, but still pulled in 350 in 6 months working part time.
If you can find a pilot mill that is 141 id say go for it if you want to be done as soon as physically possible, but the quality at Wisc Av will be higher, and if you get a CFI that can work with you every day for 4-8 hours it will be just as fast.
Most those mills are in the South, South west and West coasts. A few out east and one in chicago. But like I said, ATP isnt 141 as far as i know, but I could be wrong.