not sure
I would think it would be atleast a 24" barrel, but a 26" would be even better. The length of the barrel will have a dramatic affect on velocity of the round. There will be a loss close to 100ft/sec/inch of barrel being removed. A lot of calibers need the length to get the most velocity that can be obtained from using slow burning powders. I would think the varmint calibers you asked would need more length to perform well. Manufacturers cut cost by shortening the barrels which is why most calibers come in a 22'' barrel, but some just don't perform well with less than 24".
Since a varmint rifle is normally used in a stationary situation, using a longer, heavier barrel lends itself to more velocity and a little better accuracy normally, but not in all cases.