One problem that some kids (and especially girls) is that they have a tough time holding the gun out to point. When you think about it they are using their non-dominate arm, which is weaker to hold the bulk of the weight. Pumps put more weight out front with the mag tube, etc. Remember too that a pump will have the forearm moved forward and that is a stretch for some kids.
I would suggest you let your daughter hold a couple guns and see what she can comfortably shoulder.
I do think the 28ga is a great choice. Much more useful than the 410 without much more recoil.
I lucked out and found a 28ga Franchi 48 with a 2nd stock that could be cut down to fit. Super light, little recoil, semi-auto so forearm was no reach.
Keep in mind too that this should all be enjoyable for your daughter. No pain, no stress will increase the odds it is a positive experience. Make it fun, not a chore. A couple $$ spent (or wasted) now can pay off dividends in the future.
