You will be happy with either one. I have both, but started with the lux. Loved the accuracy once I found the right ammo. It's nice when you can't blame the gun anymore for a miss.
The 10/22 is for a different kind of shooting, get a 25 round clip or two and blast away at tin cans etc. It won't offer the accuracy of the lux, but repeat shots are readily available. Once you get it sorted, a 10/22 is at it's best shooting gophers. Since you don't live too close to gophers, I'd get the lux. Actually, I'd get the American instead, since I prefer scope shooting and don't like to be so high off the cheekpiece. For a high quality bolt action at a reasonable price point, they don't have much competition in the .22 realm.
Having said all that, it's usually the 10/22's that leave the safe, while the CZ stays at home, since it's tin can season around here.