Checking Zero
Besides cleaning any superfluous grease from the bore and wiping the outside off, the very first thing I do is check my zero to determine if the sights need to be adjusted. So yes, you check zero from the factory first rattle out of the box. When you are hitting what you're aiming at then the sights no longer need any attention.
There are issues with changing ammo. Heavier bullets tend to print higher than lighter bullets. Just be aware of that and don't let it surprise you.
If you're using it for self defense I'd find one load that hit where you're aiming at 15 yards. No need to engage someone farther than that in 99% of self-defense encounters.
If you're hunting, decide on the range you plan on shooting and zero the gun for that range. Now, all of the above is predicated on you having adjustable sights. If not, you can learn to hold your sight picture differently for different loads, though I believe that's a technique for the experienced shooter.