You’ll probably get a lot of different answers as there are lots of different experiences, preferences, etc. My background is as an NRA-certified firearms instructor for private security.
That’s an interesting path you mentioned. I could see where you could begin with fundamentals and work your way up. However, and this is just my personal opinion, that muscle memory you speak of will be completely different when you increase your caliber. Pulling the trigger will be different, the size will be different, plus the recoil will definitely be different, which will affect all of your fundamentals, especially grip.
Instead of purchasing one to begin the process, I’d recommend renting the handgun and the range time from an indoor firearms range. Now I’m not too experienced doing that because I’ve always had countryside space to shoot, but I hear guys talk all the time about doing it. You can rent the gun, rent space in a shooting bay, and buy the ammo right there for it.
You didn’t mention having a permit to carry so I will address it as if you don’t. You’ll have to go through that, which will involve classroom time and a brief range activity. That will get you some time. Then you’ll be submitting an application, as you’ll need the permit to buy your handgun. (If you wanted to purchase a handgun just to keep in your home, and you’d never take it outside your home, you could just get a permit to purchase. That’s just an application process with a background check done, no class or range training).
Anyway, I’d recommend the route of trying out different handguns at gun shops, ranges, and from people you know. You’ll see how the different guns operate and get a feel for what each caliber will do for your. If you’re able to form a decision then you can buy and train with what you’ll use. As an instructor no one ever wanted to hear me say this, but you can improve the meat and potatoes of your skills GREATLY without every firing a round. If you’re concerned with crime and will be carrying you’ll want to work on drawing from whatever holster you’ll be using. You can work on grip, stance, and sight picture all indoors without firing a round. Your aim with a pistol involves your eye, which is actually a muscle that can be trained to improve your shooting. You can work on your stance and grip and pulling the trigger all at home with a spot on the wall. Honestly in the same sense that people nowadays just want to be put right on fish without the grind of working for them, I think a lot of people want to get better at shooting by going to a range and putting bullets on paper. There is SO MUCH you can do at your own home to get A LOT better.
Let me know if there’s other things you have questions with or PM me, I’m sure others will chime in as well.