I'm old school, and low budget. My favorite 10/22 wears a simple 3-9x40 Bushnell with lighted reticle, sitting on Weaver see-through rings. Many people hate high rise rings for obvious reasons, but they do have a use for some of us.
I use the scope at 3x-4x for accuracy at mid to longer distance shots. A quick shift in cheek weld allows me to use the factory sights for up close shots.
While this approach works well for my uses, it certainly may cancel out your whole point of a take down rifle.