You get what you pay for. And yes different makes and styles of ammo will vary in accuracy. Cheap ammo will not be as consistent as that which is more carefully (and expensively) made. (Rule of Thumb, there are exceptions.) You're going to have to experiment with different ammo to find the one that shoots best in your gun.
If accuracy is your ONLY concern, gather as many different makes of ammo as you can afford and shoot them for the sturdiest rest you can find. Then you will know which shoots most accurately and potentially the smallest sized group you could possibly shoot with that gun.
If you want particular terminal characteristics, then it will limit your ammo selection. This is one reason some people reload. They can select the particular type of projectile they want and then vary the velocity (within reason) to get the optimum accuracy from that bullet/gun combination.
Having said all that, don't over-stress on accuracy. Shooting man sized targets at 21' doesn't require Minute of Angle precision.
Now personally, and I wish I had done this years ago, I suggest a new shooter start with a true target pistol. Could be a long barreled, .357/.38, like a SW 686, or it could be a rim fire, like a SW41 or a Buckmark. This takes the gun pretty much out of the equation and allows you to practice the fundamentals knowing that anything outside the X ring isn't the gun's fault. Yes there will be some differences going to a different gun, but the basics are still the basics.