Welcome to the greatest sport! You will like the 10-22, it is reliable, and well designed. I'm glad you are starting with immersion training, learn the good habits from the start; andyou won't need to unlearn vad ones later!
Ruger also makes a 4-44 that shoots 44 magnum pistol ammunition in the same form factor. It holds only four in the rotary magazine due to bullet size, and is a nice hunting carbine.
The sling is your friend, and on larger calibres, it will significantly increase your control of the firearm. All aerious firearms should have one!
The open sight is perfect, anyone can use a scope; but an iron sight will make you a better shooter. Holding your sight picture, After you squeeze the trigger will visibly reduce the size of your group on the target. It takes a finite amount if time for the bullet to travel out of the barrel, if you start to move (as is normal); to see where you hit, the pattern will open up accordingly.
Starting out in the pew, is wise; lots of people here are good shooters, and will help you along the way!
Enjoy
:)>