+1 On NOT needing a Centurion. That insurance will be crazy as will operating expenses compared to 172/182.
As
@WannFly said I did zero to PPL in a 182P model. They are tough, easy to work on and lots of room. I would venture to guess learning in a HP plane maybe added 5hrs to solo time and negligible to overall PPL time.
The 182 will be spendy but retains its value. So should you feel the need for speed after your PPL you will have no trouble selling it for a faster retract or Cirrus/TTx/RV-x.
Versus a 172 or Archer you'll burn another 3 to 4 gal/hr so if your PPL takes you 70hrs that's gonna add over $1000 to training costs. Maintenance reserves should also be considered if you purchase the plane. The old Continental motors are only 1500 TBO and using $45k for rebuild that's another $30/hr you should be stuffing away for the eventual rebuild or depreciation in value if you sell it later with a high time motor. So that's another $2200 to budget for flight training and $$$$ you wouldn't spend if renting to learn.
You'll like the HP of the 182 for your density altitudes.
If you think you'll be doing lots of trips beyond 500nm you will quickly want a faster plane.
You're also a bit cart before the horse...
Have you ensured your medical?
Where will you park it and preferably have it covered?
If you dont mind sharing. what is your budget?