The OP states that this is a home defense gun and not a CC gun.
In my book that rules out almost all compacts right off the bat.
You want a gun that is easy for you to control and that you are willing to spend the range time with to become proficient with its use.
The larger gun will also hold more rounds of ammo.
If there is a particular ammo that does not function well in your gun, that is the ammo that you want to spend some time practicing with, but NEVER use as your home defense round. That way you will learn to quickly and efficiently clear jams should one ever occur with the "good" ammo.
Since size of gun is not the issue and you say that you have big hands, I would recommend to go bigger than 9mm.
As many have mentioned, your best bet is to go to a range that rents guns and try a bunch to which ones fit you. or go to the range with some friends to try out their favorites. The best gun and/or caliber for me may be the worst for you. Some people are very recoil sensitive and some are not. Some guns will feel like a much heavier recoil with the same ammo than others. Some calibers have a lot more recoil than others regardless of what gun they are in.