Nothing wrong with pursuing a medical career and being a private pilot. I have a junior hospital doctor (an orthopaedic surgeon) in my C150 group and he did a large chunk of his training with the London University Air Squadron while a medical student (though he completed his PPL after qualifying). He loves to fly as a complete contrast to his day (and night!) job.
We also have a couple of commercial pilots in our group and they love to fly our humble C150 for the same reasons- It's just fun.
If you decide to go down that route rather than the professsional aviation route it might be worth looking for instruction somewhere that focuses on private flying rather than training the next generation of airline pilots. I did my PPL at Clacton Aero Club and if a flying school/club advertises things like tail wheel conversions and its instructors don't dress up as captains you kind of get where they're coming from.. Having said that, at least one of our commercial pilots started out with the intention of just being a private pilot so where you start isn't always where you end up!
I'd suggest visiitng a few clubs and just getting a feel for them before committing.