Gun fit is very important, especially if you would really like her to shoot. Inexpensive makes things much more difficult.
20 gauge can be a handicap, especially if you plan to shoot the clay target sports with a new shooter. Recoil is relative to the amount of lead that you are pushing down the barrel, velocity of the load and barrel bore diameter.
Felt recoil is primarily dependent on how well the gun fits the shooter. This is probably the key factor.
I would suggest a 12 gauge 1100. Look for one with a short, choke tubed barrel. There are a ton of used adjustable stocks and barrels available. If you buy used at the right price, you will be able to get your money back out of the old 1100 when you sell it and she moves on to the next level.
Bill Malcolm