I think the 1100 is a good place to start. They are fairly simple to keep running and if one needs parts, they are easily and cheaply found. They are also pretty soft shooting and, as mentioned, people seem to shoot them well when starting out. A light O/U or even recoil/inertia operated is going to kick a fair bit and your daughter has already mentioned this as something she wishes to lessen.
The 1100 is very easy to adjust to women also. I learned from the Remington Shooting School (before it combined with Orvis) was the small framed 20 ga guns could be fitted with the 742/7400 stock meant for their semi-auto rifles. (The 760 stocks can be used on the small frame 870s) These have a higher comb which women tend to need plus a little shorter length of pull though they don't have a recoil pad which would negate the shorter LOP. That isn't a problem as removing wood, from either or both the comb and butt is easier than adding.
If one is using the old pre-1977 standard frame 20 ga which uses the larger 12 ga frame one can sub in a trap stock for much the same purpose. I did this with both my large frame 20s with good results.
Getting a rough general Fitting isn't rocket science but it isn't the easiest to do on one's own the first time. Hiring a certified shooting instructor should get you started in the right direction and he should be able to recommend a competent fitter, hopefully locally. There are a number of books one can read to get the gist but having someone experienced do the first one helps connect the dots quicker.
