PPL and time building in the US - which school?

[B2N2]

Here’s my bit;
I agree with all of the above except picking a random school or shade tree Instructor.
Cheap does not equal good in aviation.
Find a school experienced with European students and especially differences in logging between the USA and EASA.
For example under FAA you can log your Intrument Training as PIC since you are rated in the airplane.
Last think you want is going back to EASA land and being told your hours are logged incorrectly and you need to redo part of it.
So use either two separate logbooks or one where you log the differences.
As FAA PIC ( can be with Instructor ) and EASA PIC ( can not be with Instructor).
Also look into the cross country requirements for the EASA CPL.
When you’re smart about it you can easily fly all the requirements during your time building.