Check both the 10/22 and 795. Get what SHE likes the best as she'll enjoy shooting more.
I always like the "Well the Ruger has more accessories" argument. If money is a concern then it doesn't matter now many accessories there are. Plus, there aren't as many for the 795 or 60 because they don't need them.
(j/k)
However, you can accessorize if you want to. See here:
http://www.gunandgame.com/forums/marlin/82869-marlin-60-795-accessories.html
My wife likes her 795 over a 10/22 for the following reasons:
1. Lighter (795 is 4.5 lbs)
2. Easier to change magazine and load a round in the chamber (She hates the Ruger mag "safety feature")
3. Dead accurate (15 round nickel size groups off a bench)
4. Can paint the stock to her color preference (btw you can get wood and youth stocks for the 795 and total cost will still be less than a 10/22)
What I liked:
1. Rifle cost $105 after rebate from Dick's.
2. Tech sights were easy to install.
3. Comes equipped with swivel studs.
4. Frighteningly easy to remove action from stock for cleaning / lube.
Both the 10/22 and 795 are good rifles. Neither is perfect, but both are dependable and durable.
Alemonkey
Either one will be plenty accurate for Appleseed. You really only need to be able to shoot 4 MOA consistently. For 99% of shooters it won't be the rifle that holds them back.
What he said.