I use my Mossberg 500 pump for all the above.

benelli pump the best pump i own great all wether gun easy to take down and put back together and the recoil reducer option is excellent for big loads like turkey loads, buck shot or slug for deer.I personally have put over 25000 rounds through mine everything from 9 shot dove rounds to 000 buck. as for larger game than whitetail i would go with a rifle 243 or greater more stopping power and penetration for large game with thicker skin. GOOD LUCK OUT THERE

223. It might be hard to shoot a turkey with it but it will bring down a deer.

seeing as you want to hunt both deer and turkey you'll need a shotgun with probably .12 gauge as a safe bet. Then you'll need to buy some quality slugs to shoot with them.

I'd suggest the 835/935 mossbergs(pump/semi). Both will shoot up to the 3.5in shells and WILL take down ANYTHING in North America(limited range though). The 835(I have)has a "ported barrel" which reduces recoil, the 935(auto, reduces too)not sure about the barrel though(don't have, yet). That and a "good" slip on recoil pad you should'nt have any problems.
Good Luck and Good Hunting !

Sorry about the double post.

Try a benelli nova 12 ga. if you don't want to spend more than $400, but if you do try a benelli m2 if you don't shot 3.5" shells or sbe2 if you do. I have both the nova and m2 and I have hunted deer, turkey, doves, duck, geese, and coyotes with them. Won't trade my m2 for any other shotgun.
If you can hunt turkey with a rifle try a Ruger M77 in 30-06 or 7mm.

I would use either an 870 combo or a 500 combo I own one of each and I like the Remington 870 better but it is just a personal prefference

The 870 is the most popular shotgun of all time for a reason. Have had good luck w/ Mossberg's too. Both a good value.

Given that mix, I'm going to vote for a Remington 870 with both a shotgun and a slug barrel.