Employers don't care where you got your ratings (unless it was in the military). They just care that you have them, plus whatever flight experience they require.

Don't pick a school because you think airlines will hire their grads...that is BS and I would walk away from any school which tells you their grads are "preferred" by airlines.

Select a school based on safety, reliability, and cost effectiveness. A more expensive school in your hometown might be better if you can live at home and keep your day job

No, nobody cares. I have trained and instructed under both 61 and 141. 61 is usually more cost-effective, since it is far more flexible. 141 can force a student to keep practicing skills he has already mastered because it requires adherence to a rigid syllabus. IMO 141 is usually only beneficial to military veterans using the GI Bill...which requires the use of a 141 program.

Historically, nobody cared except that some employers required a certain amount of instrument time which you will not get in the desert. In the past simulated instrument time was acceptable, but congress appears ready to change the requirements for airline pilots (but not other commercial pilots) to require a certain amount of actual instrument time. Nobody knows exactly when this will take effect, but if I were starting out I might look for location where actual instrument conditions (IMC) are common. Also make sure the school allows students to fly in IMC.

I've never heard of transpac, but ATP is somewhat reputable IMO...they are not crooks, which is saying a lot in the flight training industry.

Also be aware that the airline hiring practices and consequently the flight training industry are likely in for some big changes due to congress. Nobody knows for sure what the final rules will be, however you may have have some new, additional requirements to work in the airline world...

- 800-1500 hours total time. Most flight training programs provide less than 300 hours.

- Significant time in actual icing and IMC conditions. Trainers CANNOT fly into icing conditions, you will need larger, more complex, and powerful airplanes for that. This means effectively that you will have to work for a charter, freight, corporate, or private owner. You cannot qualify for or get insured for those jobs without at least 1000-1200 hours so you will need to work as a CFI for 1-3 years first.

- Significant Multi-engine time, possibly several hundred hours. This could be acquired as an MEI, or flying advanced airplanes (see above).

One significant factor to consider when selecting a school is will they hire you as a CFI when you are done? Schools usually prefer to hire their own grads, so if you don't get hired by YOUR school you may have a harder time with other schools who will hire their own folks before you.

Be careful...large puppy mills (like ATP) may have a policy of "hiring" essentially all of their CFI graduates, but there will not be enough work to go around and you only get paid when you work. You might fly once a month, which will get you nowhere fast career-wise.

A smaller school which teaches a lot of recreational students may be better because there will be fewer career pilots competing for the CFI jobs.

You have a lot of homework to do, search these forums for old posts and keep asking questions.