I prefer the new Marlin Papoose for a survival .22LR rifle. Generally I think bolt actions of a more powerful caliber would be the best choice for durability and simplicity in a survival rifle, but if I am using the .22LR I would want an autoloader to get off multiple fast shots if I need to. Given the marginal effects of the .22LR on medium sized game past 50 yards it will probably take more than one to finish the job. A lever action would be next choice but I haven't found one that has the features I am looking for.
Why the Papoose? Because its portable, durable, reliable, and is versitile. Mine gets sub quarter sized groups with CCI 40g RN Mini Mags and is 100% reliable with it. I personally feel that heavy, high velocity round nose is the best choice for a survival .22LR. It causes less destruction on small game than HP and it penetrates larger animals better.
I attached a picatinny rail on mine to accomidate standard scope rings, I currently have a 1.5-4.5X bushnell scope and I am working on getting some backup peep sights. I have an SU-16 rear sight that works perfectly and I am going to get a front sight assembly from Tech Sights. Additionally the stock is hollow and I can put 200 rounds in plastic bags in there. I also have a modified shotgun stock shell holder that fits five 10 round magazines in it. So I can have a gun with optics and and 250 rounds of ammunition in a small bag that weighs about 6 or 7 lbs. I would just throw this bag in my larger survival pack with other neccesary items and I would at least have a rifle if I needed it.