My first thoughts would be something like a 10/22 takedown, or even Marlin 70 Papoose, given the added utility. Handgun-wise, can't go wrong with the classic Ruger Mark-series.
Likewise, can't go wrong with any of the name brand .22 bolt guns. Marlin XT-22 (I'm partial to it), Ruger American .22, Savage Mark II.
In all honesty, if I had the cash, I'd like to do one of all 3, a semi rifle, a handgun and a bolt gun, but again, for the utility, I'd probably do a 10/22 takedown...