"Starter" rifles...
Jeannie 29--Good on you wanting to take yr daughter hunting, and for that matter wanting to go yourself!
As has been stated, PRACTICE is the thing that makes good shots--If you can find a .22 rifle that both you and your daughter can use for practicing, you are 'way ahead. Otherwise, if you are quite tall and she is quite short (for example) you will have to get rifles that fit you separately. Yes, "fit" IS that important.
But the more you shoot, the better you get. .22 ammo is relatively cheap, and the skills you develop shooting .22's at tin cans transfer directly to shooting bigger rifles at deer.
Now, as to a deer rifle, I went through the same thing with my #1 son when he wanted to begin deer hunting, at age 11, and we ended up getting him a "youth model" .243. He could handle the recoil, and became quite accurate with it. There are a number of "youth model" rifles out there--However, don't hope to find one used--what happens is that somebody buys one for their kid, and then all the nieces and nephews use it, and then it goes to the grandchildren! They just don't come on the used market very often, we found. Of course, my son didn't mind at all getting a new rifle, just I minded paying for it!
If you yourself are smallish, you may be able to share the deer rifle with yr daughter, just like the .22, but you may need an adult-size rifle--you'll have to determine that. I'd say look into that AFTER you have been shooting .22's a while.
As TX 1911 Fan stated, the .243 is very easy to handle for recoil. That's why a lot of kids get started deer hunting with it. I would NOT start a kid on a .30-'06 of any description, or a semi-auto 12 gauge, or a semi-auto .270--semi-autos are heavy to lug around the woods, and while the semi-auto function will lessen the recoil, .30-'06, .270, or 12 gauge is still too much for any beginner who is not built like a football lineman. For a kid, light is right--she needs a bolt action, or a break-open action, in a smaller cartridge. And probably, so do you.
The bad news is, all that will cost money. The good news is, that you, and husband, and daughter, have an exciting adventure ahead, working together to get fitting .22's, getting good at shooting, and then finding deer rifles that fit. And then practicing with the deer rifles. And then going deer hunting.
It's a great adventure! I envy you the starting of it!