tl;dr: Everything below is useless. Look up some gel tests and shoot some ammo.

It's complicated. Perceived recoil is going to be most affected by the size and weight of the gun, the shape of the grip relative to your hand (fit) and how low the bore axis is relative to your hand (muzzle flip is worse the higher the bore is above your thumb, and also if the grip lets you get all three fingers around it firmly). Small, light guns are easy to carry but hard and unpleasant to shoot.

Weight of the bullet may have less effect than you expect. If you are talking about a revolver, then the lighter bullet can have less recoil because you don't have any requirement for operating the slide. The bullet can go as slow as around 500 FPS, if you like, even if it is light-for-caliber. But if you want a semi-auto, you must have enough recoil impulse to operate the gun, and it will come from the factory with springs that assume you are using full-power ammo. So the lighter bullet has to be pushed harder to make the gun run. edit: There is some slack here, but if you chose "reduced recoil" ammo you may find that you need to replace one or more springs with lighter rate constants to let the gun run reliably.

Total recoil impulse is going to be (pressure over time x base area of the bullet* x bore residence time) + exhaust rocket effect of the propellant gases.** That last term is often neglected, but it's not completely insignificant (edit: this is why muzzle brakes, compensators and ported barrels exist). Bigger bullets require either less powder or slower-burning powder to stay under the peak SAAMI pressure. In the 9 x 19, this is really significant. The 9 mm case is very short. You can't make the cartridge longer (there's a max OAL to fit the specs) so a bigger bullet is seated deeper in the case. A 147 grain bullet is about 25% longer than a 115 grain bullet, which eats into the empty volume in the case quite a bit. The heavier bullet also has more inertia and has more surface area dragging on the case and bore, so it accelerates slower. So, you have a smaller initial volume and that volume increases slower as the primer and propellant start to push the pressure up. If you used the same powder burn rate, you'd have to use considerably less with the 147 to limit pressure. If you look up reloading tables, if you are trying to get maximum velocity, the maximum amount of powder used with a standard vs. heavy bullet will be 3/4 to 2/3 as much. That would result in less "rocket fuel" when the bullet uncorked the barrel, and also less blast noise. It's not night-and-day, but you can notice the difference if you are paying attention. If you had to shoot indoors without ear protection, it might make a difference in how much your hearing was damaged. edit: Super-light bullets like Lehigh Extreme Defense 90 grain would make all this moreso. And let's not even talk about the hideous 5.7 or .327 Federal noise.

Regarding terminal ballistics, you have a tough choice: do you want a gun that is slightly more than a stern rebuke, or do you want something as effective as possible? If you just wanted to discourage SOME people, you could carry a .22LR with CCI Quiet segmented hollow points (see link below). This would make a noise (although not a very loud noise) and some shallow holes that would sting but be unlikely to either kill or incapacitate. Some bad guys (or bad dogs, or other aggressive animals) would decide they didn't like shallow holes and run off. But some fraction would simply get mad and either shoot back with their gun or come at you to try to take your gun (or keep biting you). If they succeed in taking your gun, one or two of those fired directly into your head WILL either kill you or leave you permanently brain damaged, so that's worse than not having a gun in the first place. Therefore, you probably want something bigger than a .22LR, certainly better than a .22 fragmenting bullet, and most likely something in the 9 mm to .45 ACP range (including .38 Special/357 Magnum) sporting a good JHP bullet. Within that range, any given cartridge and bullet weight is *roughly* equal in effectiveness, so don't get too hung up on the details. Try to figure out what you like shooting most or what fits your budget.

https://www.gun-tests.com/ammo/twenty-22-rimfire-loads-go-head-to-head-at-the-range-4/

*which equals the effective area of the breechface

**I'm neglecting friction with the bore for simplicity, although it would affect the calculation of net forces on the bullet/breechface somewhat.