You can use both cal for deer. I would go with the 06, cheaper price for amo than mag amo, 06 has been doing the job on deer for over a hundred yrs. As far as a rem 770 go'es check out other makes in that price range.
Mossberg, savage, They all have combo units for sale too.
I'm still learning here and there. just wondering what would be better as far as barrel length. 770 comes in 22",24",26". I do believe that the longer the barrel the further the travel,