What I would do, maybe, is pick up a Ruger 77/22 hornet with the gray finished metal and laminated stock, set the barrel back enough to get a clean minimum spec chamber, then cut off whatever is beyond 20 inches.
The reason I said "maybe" is that the Ruger magazines won't handle the length of the 40 grain VMAX and Ballistic Tip so you have to single-load those. Of course, you don't HAVE to use the magazine. A buddy of mine from Colorado used a Ruger 77/22 hornet loaded with AA#9 under 50 grain VMAXes, single loaded, as one of his primary p-dog guns. Can't argue with results.
There are probably better rifles to start with but most of them use fugly cheap looking stamped metal magazines which stick out from the bottom of the gun. That's a look I just can't stand. I'd go with a single shot first. And, in fact, if you can find a Ruger #1 in .22 Hornet that'd be a good choice. Another good choice is a Thompson Center Contender carbine with an aftermarket barrel ... I like Bullberry.
I'd look really hard at K-Hornet instead of a standard hornet just to have it headspace on the shoulder, not the rim, hopefully improving case life a bit.
