I'd probably choose this one in .22 Hornet
This is a nice rifle that I wouldn't mind owning. Thinkin it's a Annie. I guess if the range was close enough it would be fine for coyotes and small meat deer, and definitely up to the task of perforating paper out to a couple hundred yards.
Following this lead, move up the next step in range to a Sako Vixen in .222.
Then, a little more range and versatility. Slumming a bit, but another super short action length with a 1:8 twist X-Bolt in 223
I'd skip over the fast 22's, but I'm sure a case could be made for them.