Before I try and help you with your sight situation I will just put it out there as fact that a receiver mounted optic on a 10/22 Takedown will never hold zero. I have owned and played with a total of six Ruger TD's over the course of a few years in all kinds of configurations.
POI is usually off by about 3/4" after disassembly/re-assembly no matter how tight you adjust the lock-ring. This isn't a big deal to lots of folks and you can still hit a pop can at 25 yards when you re-assemble, but it is what it is. I have come to the conclusion that a good quality Micro red-dot on top of the MagPul mount along with quality irons is the premiere set up for a 10/22 Takedown. Accurate as any bulk rimfire can be out to 100 yards and totally repeatable when breaking down.
Now,on to your question about irons, you would be well served by the Skinner barrel mounted combo. My eyes aren't so great anymore and I am still able to get a decent sight picture with them and do good work.
If you are running factory included base/rail then you need to ditch it in favor of an aftermarket low rail with a deep groove to pick up your sights, I would recommend the Tactical Solutions rail for this, but you could get by with a cheap Chinese Monstrum or UTG off of Amazon I believe,as long as that deep sight groove is present. The Leupold rifleman base is also suitable but not as versatile with only a few weaver slots.
The "Williams Ace in the Hole" rail and sight combo is my personal fave and is the lowest rail made that I know other than the Leupold rifleman of for the 10/22, but if you need the extra rail space for your rear scope ring where the peep-sight ramp is you're SOL.
Here's some pics of the aforementioned parts. Williams Ace in the hole rear peep and rail with a fiber optic front sight. Tactical Solutions picatinny rail, Magpul backpacker barrel mount and a Skinner barrel mounted combo.
Hope this helps!