I’m a bit partial to the Piper line, Cherokee of some flavor or Warrior. That said, I wouldn’t rush into buying a plane anyway. Ownership would be more of a distraction to ‘faster track’ flight training.

Can you go off to a flight school somewhere & move things along in a timely fashion?

When learning to fly there’s little need to push buttons, G-1000 or whatever. A little steam & learning the basics of flying is what you need.