In the end, only you can answer the question, because it's really about what floats your boat.
The idea of getting a rifled barrel for the 870 for deer hunting is sound -- I used to hunt in Tidewater Virginia, where shotgun-only was the rule, and I have killed many deer with a shotgun.
If you intend to get a Concealed Carry permit, then the handgun is the best choice (along with the rifled barrel for the 870).
On the other hand, a rifle will give you more capability when hunting. I would go with the Savage over the Remington -- the Remington 710 is made to be cheap to produce and looks it. The Savage was also designed to be cheap to produce, but has racked up an enviable reputation for accuracy and performance. With the Savage Accu-Trigger, it will be all the better.
And for what it's worth, you can change calibers with the Savage -- Midway USA sells conversion kits. The first kit will require a barrel vice, barrel nut wrench and action wrench, but later conversion kits only require the new barrel, magazine, and headspace gauge.