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Only issue with that is 10/22s are shit unless you spend lots on them, where as Tikkas out of the box are stupidly accurate and smooth and have good triggers, especially considering their price.
I...

Just go Tikka T3 Varmint.
Second hand ones come up every day or two on Trademe, you could literally change caliber once a week.
Heaps of aftermarket bits which you can switch between rifles, due to...