HoneyDutch, welcome to TFL.
The first question I'd ask is, what kind of shooting interests you? You may not be sure yet, which is fine, but if you're attracted to hunting as a longer-term goal, we'd likely give you a different set of suggestions from what we'd suggest if you're thinking about home defense, or eventually carrying a gun for self-defense. If you just want to get started, plinking and target shooting for a while, you should get the type of gun (likely a rifle or handgun) that interests you the most.
Another question: what kinds of places do you have access to for learning/practicing? That's going to determine what kind of shooting it's practical for you to do -- if you just have access to an indoor range, you're going to be limited in the distance you're shooting, compared to what you could do if you or a friend has acreage in the country, or if you can get to a good outdoor range.
If you do have a shooting range near you, someone there probably offers instruction. One of the best things you could do is to sign up for a class or two before you actually buy a gun -- you should be able to rent or borrow a variety of guns, which will give you a better idea of what you like. (In any case, you should plan on getting some training as soon as possible.)
As to "which gun," pretty much everyone who answers you will give you an answer based on personal prejudice.
I'm no different, so I'll say that your first gun, IMHO, should be a bolt-action .22 like the Savage MKII. They're very accurate, cheap to shoot (at least in principle, and ammo prices/availability will come back to normal sooner or later), and have essentially no recoil --so you can shoot a lot without going broke, and focus on learning good technique without worrying about developing a flinch or other bad habits that can be hard for a beginner to avoid with the larger calibers. (You're right -- that .357 revolver isn't ideal to learn with.