Well, first off, what's your price range?
Second, is this a dedicated turkey/deer gun, or also upland bird/waterfowl?
You can buy a rifled barrel for your Remington gun from Ithaca, cost you approximately $125-150.
If you want to spend 350-600, look at Ithacas, Benellis, Berettas or the 1187SPS is a nice gun.
We also don't know if you have a scope, plan on getting a scope, and which type of scope you may/may not have.
If its just turks & deer, I would suggest at least a red-dot, if not a full optic scope.
I just setup an Ithaca Storm, with rifled slug and ported turkey barrels, topped with Tru-Glo fiber optic sights. Picked up the gun as a promotion from Ithaca for $500. However, I'm in my mid-30's and wanted to get a scope...the eyes are still 10-20 & 20-20, but my dusk vision is wandering. Hence, I just ordered a 3-9X40 Burris FFII with spotting scope ($190) from NatchezSS (on sale), with a B-square mount and Burris Sig Rings ($60 total). Total package ~$800 after the shipping and fees...
You can reach out to 150 yards with Sabots through a rifled barrel, hence my decision for a high mid-range $ optical scope.
Some more info would help...