Definately go with the 22 Hornet, if you are into reloading make it a K-Hornet, the velocity increase is mostly imaginary, but the round is a bit more accurate because of the shoulder to headspace on.
One factor with the Hornet that most people overlook, it is quite possible to stuff 50 or 60 rounds into your jacket pocket, try that with your 22-250 <BG>
I am currently building my 5th or 6th ( lost count ) Hornet.
I like 'em jes fine <s.
Jim
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Lay up some blackpowder and flints
The rest we can build, if need be