One of our guns is a Moss 500 bantam. It is a smoothbore with a Imp Cyl choke. 20 gauge. It is strictly a slug gun. I do have a turkey choke and a normal choke availible for it.
With that in mind, my answers to your question regarding rifled barrel is probably going to be sabot rounds for you. They can carry the same as my slugs in weight and enjoy better accuracy and stopping power.
If you intend to fire bird shot, double ought or any kind of other shot, be very careful to select ammunition specifcally designed to be fired from your rifled barrel. When I select ammunition, I try to stay with those that can be used in a smoothbore first, choke second consideration followed by size and then ballisitics.
In fact I just edited this post banging my head wondering why I bother to talk about bird shot in a HD gun? You are only going to make the intruder very mad-mad and add greatly to your interior repairs.
2 and 3/4 Ammunition are perfectly ok. If you are going three inch... it seems to me like a Magnum round. Check your Owner's manual. If your gun is specifically stamped to take 3 " rounds, then I dont see a problem. Again, check your ammunition for compatibility with rifled barrels.
I will also think about wear and tear on your rifling, cleaning experience and possibly a spare barrel if one is availible.
That is all for now while I research the other questions you have raised. Dont take my words as gospel, we are new gun owners as well and are learning our way slowly and with caution.
One great fear we have is a 12/20 burst. Because there are two different gauges in our home, wife has her own ammo box for the moss and I have a 12 for my 870. Great care is taken not to mix ammo in different gauges like trying to shoot a 20 gauge in a 12 gauge gun.