For a true HD gun simpler is better. Self defense is not a game like 3- gun matches, there are no second chances. If self defense is the issue the gun should be kept simple, stone reliable and USED AS IS in gaming or training. The issue is the skill set of the operator, not the stuff bolted on the gun.
I have found 1100s reliable enough for HD as long as they are properly maintained. That can be a big caveat, pay attention to the manual and to reassembly after cleaning or the gun will not run. Pumps generally run as long as the operator maintains proper operator headspace and timing and doesn't short-stroke, load shells backwards etc. If recoil is not an issue the pump is a definite contender, the choice is the shooter's.
The youth model synthetic 1100 20 ga. is pretty light, haven't had hands on the wood stocked model. Keep in mind there are fewer choices for HD loads in 20 ga. than in 12, I don't know of any reduced recoil buck and slug loads for the 20 as yet- someone please correct me if I am wrong about that. With a lightweight gun and full house loads recoil is apt to be more not less, it could be a 12 with reduced recoil loads might work just as well. Try the options and see what works, that's the best way to make a decision.
As to gun mods/accessories, I would first make sure the gun fits the shooter properly no matter the gauge or action type. Stock length is critical, usually drop and cast is not so much a problem. Curves in factory pistol grips are often too deep for small hands, make sure the trigger finger can reach while the rest of the hand can maintain a strong grip on the stock. The area can be built up as needed and relieved for proper grip. It won't be pretty but if you are going to paint it blue anyway no one will notice.
Keeping weight off the front of the gun is a big factor with smaller shooters. Consider doing without a mag extension or keeping it as short as possible if she's just gotta gotta have one. A SideSaddle puts weight between the hands and seems not to be as noticeable as more weight out front. There are 4- round versions available now that are even lighter when loaded, I really like having extra ammo on the gun no matter how it is carried, and like SideSaddles best among the available options.
Shorter shooters have shorter arms, make sure the fore-end is where it can be reached without hyper-extending the support arm. Also make sure it can be grasped easily, it might need shaving down to provide a good grip.
Sights are an either/or on a HD gun, unless the fight might go outside. For a genuine house gun a tritium bead will suffice IMO.
A white light source can be helpful, but shouldn't require a massive overhaul of the gun. With properly set up house lighting and a barricaded defensive position any intruder will be a target silhouetted in a backlit doorway, searches to ferret out genuine intruder noises are generally a poor idea IMO.
As far as the gun is concerned reliability is the utmost concern, for the shooter developing a solid skillset covering the basics is crucial. That requires lots of hands- on and trigger time, putting lead down range and on target is the key. Not much else makes any difference...
hth,
lpl/nc
Reliability, ease of operation, extra shell/s, lighter weight, and better sights.