Learning to play kit, came naturally, but it was somewhat secondary. I first was introduced to drumming with a practice pad. Not even a snare drum. Got into band in school, then the parents bought me a REMO pre-tuned snare (wretched sounding). Then I got into Jr.High jazz band. So, I was given a pawn shop kit--and that darn thing stayed with me through college.
C.M. and I had similar upbringings, but I had NO drum teacher. I had my music teachers in school, and then once in marching band, I really started picking up a TON just by practicing for 12 hours a day with the drum corps. You know, if you want to JUST learn to play kit, buy a kit. Nothing wrong with it. There's NO right way.
I agree that there's no fixed approach. Different schools of thought promote different introductions to drumming. Even so, in my silent musings, I thank my first instructor every day for enforcing a pad-only/snare-only system for a few years. Rudiments can be tough to gain if you don't do it early. I've met several very serviceable drummers who, even after years of playing, still struggle with double-stroke rolls, alternant flams, paradiddles, and other complex sticking patterns because they played backbeats for a few years on drum sets before they ever attempted a rudimental exercise. These days, I'm mostly a backbeat drummer myself, but I'm glad I learned to do a whole lot more in my early stages.
Looking back, I definitely wish I had taken "lessons". Honestly, I'm still considering it nowadays. Of course, a personal non-online teacher isn't going to go over right now.