Here is my Marlin 795 with Tech Sights and a Boyds stock; I shot Rifleman with it at an Appleseed last year. My brother did the same with his 795, Tech Sights and a standard stock. I don't find the magazine changes to be a problem and for whatever reason I'm not a huge fan of the 10/22.
The sling is from the Appleseed web store if I recall correctly. A cotton sling is easier to work with than a nylon sling because you can get it tighter without discomfort. You'll want a sling like this if you don't have one, it helps. The Tech Sights are a huge plus, too. The stock is a nice upgrade but not necessary.
Something like a S&W M&P 15-22 would do well, too, but that won't solve the price problem. You can get 10 round mags for it which makes prone shooting easier. I'm going to try mine next time I go, I think.
Apologies for the picture size, I can't change it easily from my phone.