I was going to stay out of this because of my oft-noted bias toward the various 'walls when thinking of single shots, but since waterman already mentioned it...
I, too would put my vote in for the Winder 3rd Model Musket (low-wall) IF you can find a beater with a good bore or a good one with a bad bore; in short if you can find anything you could use as a donor for building. I choose the musket over the standard low-wall because the stock is the same on the former as for high-walls, so it is possible to build a full sized rifle on this action without having to trim down the wood so much. The barrel threads and breech ring are big enough to take a #3 or larger barrel also. I have made a .22 rf sporter out of one of these actions, even bending the lower tang for a pistol grip stock, and I am quite happy with the results.
You could do all of this with a high-wall .22 as well, but the high-walls ALL seem to cost more than the fairly numerous low-wall muskets, and the four holes in the side of the low-wall's receiver make it less attractive to those wanting a custom rifle...I just put four plug screws from Brownell's in mine!
Finally, the low-wall concept was designed to make it easier to load the tiny little rimfire cartridges into the chamber...not an insignificant consideration when shooting quickly before conditions change, or in the cold, or...
That's MY story and I'm sticking to it!
Froggie