Combinations are a very versatile bit of gear, but there are better ones than the Savage 24 IMHO. One major downside of this gun is that you don't have the instant availability of the two barrels, nor can you instantly fire the second barrel after the first. Instead you need to operate the selector and cock each time. I have also used a Tikka combo (also made for Savage at one time) which had a similar problem, though the .222 barrel it wore was very accurate.
I have a Brno ZH304 myself, a 7x57R/12 ga combo, and I have used it for everything from small game and birds to deer. Unlike the above it is hammerless and has two triggers, so you can instantly choose barrels or fire the second as a follow-up. This is tremendously handy, and the rifle barrel is quite accurate enough for the purpose - less than 1.5moa for three shots (I have a Sightron SII 1.5-6 scope on it). A mate of mine ended up buying one like mine, and he has barrel sets in both 7x57R/12 ga and .22HP/12ga - the latter groups well under 1 moa. There were combination barrel sets made in various other calibres, and 12ga/12ga and 16ga/16ga sets too, and they are designed to be interchangeable without gunsmithing. This model isn't made any more of course, more's the pity, but I think it'd be worth looking for on the used market.
The Baikal/EAA IZH 94 combo would be another one worth considering too. I have an IZH 94 double rifle in 9.3x74, and it is an honest functional piece.