The 10-22 is a good choice, but not the only one.
I have a Mossberg 795 LTR that I really like. It's not as easy to modify as the Ruger because there aren't as many aftermarket options, but the LTR version has very nice adjustable aperture sights out of the box and a military web sling, and is great for learning the fundamentals of marksmanship. It's actually designed specifically for that - LTR = Liberty Training Rifle. If you can get one new, the Appleseed Project will let you go to one of their events for free, and their instruction is top-notch. I went with my LTR and got my rifleman patch, and it was a great time, and I learned a LOT about how to shoot from practical field positions and how to use a sling to stabilize.