Big Donnie.....You need to check a Recoil Chart and get an idea of the recoil in the different Caliber Deer Rifles available....if Your shooting a Shotgun guess Your already familiar with recoil?
I have a Remington 30-06 and it has some pretty good recoil,my Browning .243 is great and it light on the recoil....my Savage 7mm-08 Model 111 GCNS Bolt-Action is light on recoil also,shoots good and far and has some great knock-down power.I usually put a Leupold Rifleman 3X9X40mm matte-black scope on my Rifles...runs about $175.00-$225.00 for a very nice clear scope!
Another light recoil Rifle would be the 30-30 Lever Action Rifles and with the Hornady LeveRevolution Ammo You can shot further out with a 30-30 Caliber and have light recoil in it also.
What State are You Hunting in....and what Game Animals are You planning on Hunting,just Deer or others?
With most Rifles on the Market that come with a Scope Package Your better off buying a nicer Scope and rings and bases and have it mounted,bore-sighted and then You can head to the Range and get it sighted in!