Shotguns having 3" chambers will readily handle 2-3/4" shells. The main advantage of 3" shells is that they throw more shot, mainly for hunting waterfowl (ducks, geese) where shots at long distances are more common. Most US hunters of other game use 2-3/4" shells for hunting. It's safe to say that in the US, most shotguns with 3" chambers will never fire a 3" shell. Unless its owner is a waterfowl hunter.

The shotgun needs to be certified for it. If it is approved for steel shot, then it has a lily (in German 'Lilie' - check in the internet for 'Stahlschrotbeschuss').

I tend to really enjoy shooting my 12 and 20 gauge scatterguns.

I will say that my 12 gauge coach gun kicks harder than any of them except for my 3.5” 12 gauge pump turkey gun (Mossberg 835)

The coach gun wasn’t fun until I added a slip-on recoil pad. It increased the length of pull, but it doesn’t beat the hell out of my shoulder anymore.

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@DWalt Thanks for the info. That is good to know. In that case getting a .3 inch 12 gauge would be an option even it is going to be used with 2.5 shells only. For target/fun shooting the bigger shells have usage. The extra power is not neede for target/fun shooting anyway and the same goes for self defense. .3 inch shells also would be way more expensive than the 2.5 shells.

@Bumpus13 Thanks for the advice with the recoil pad. It is a very good advice. Back then when I had my first 12 gauge the recoil was really unpleasent. Not unbearable but I would not be mad if i can find ways tor reduce the recoil a bit.

Do you guys have experience with using slugs in coach gun? I would be interested ingetting some for target/fun shooting but not sure if is a good idea to use a slug in rather short barreled shotgun. I would rather not use them for self defense because it would be overkill and I am also a bit worried about overpenetration. The homes in austria have thick walls of concret so the risk of overpenetration is not so hight compared to homes with thinner walls but who knows. I would not underestimate the power of such big lead projectile.

I have read that foster slugs are less lickely to overpenetrate because they are made of very soft lead and would expand rather fast when hitting a soft target. Does anybody know if that internet info is correct or not. if is correct I would get one of these for target fun shooting. In case I just have some slugs ready for defense it is better to have the least penetrating slugs already in case there is no buckshot or bird shot ammo around.

My first choice for home defense is always going to be some buck or birdshot the slugs would only be plan B when for some reason there is no shot ammo around.

A few thoughts:

No gun is any good without ammunition, so a 20 gauge may not be the best option for you. Besides, you have made your decision.
Too bad, because especially with two barrels, I would guess the 20 would make an easier, handier, faster handling gun for a woman. Recoil isn't an issue for me, since I am a big boy, so I enjoy the 12, 16, and 20 for their individual qualities.

You can only worry so much about overpenetration. No matter what the payload, shot or slugs, and no matter what your walls are constructed of, errant shots could go through a window or door, unless those are fortified as well.

"Chaparral Arms Wyatt Earp 1878 Coach gun at sale next week hich grasped my attention. As I said above I am into These old old west type guns."
For home defense, I would pick a gun based on performance, not looks, "cool factor", etc. Above all else, you want a reliable gun. I am not familiar with the Chaparral Coach Gun, but if it's an older gun, it almost certainly isn't suitable for steel shot.

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