I do not think that the Remington Model 7 will fill your bill. It is designed and sold as a light weight carbine, with a lighweight short 20" barrell, and is butt heavy. On sandbags, they generally get 1.5 inch groups, and sometimes 2 inch groups. This is a great rifle for hunting, especially in woods and mixed fields, but it is not a great rifle for target shooting or marksmanship with open sights. Go with a full size rifle.
Big Paulie