JDJones,
Generally the larger the barrel shoulder is the more weight you can have hanging off your receiver, at least to the structural limits of the receiver.
For receivers with a 1" diameter thread like the Rugers and Winchesters I would recommend a minimum of a 1.150" barrel shank and would prefer a 1.200".
For the Rem, Wbys and anything else with a 1.0625" thread diameter I like a 1.200" as min and prefer a 1.250" diameter barrel.
Basically, I like my barrel shoulders to be at least 0.065" deep.
The larger the barrel diameter the stiffer then will be. Again, barrel length plays a large role in stiffness but for a given barrel length, the larger the diameter the stiffer the barrel.
I never recommend using a barrel that is larger in diameter then the receiver unless the receiver will be floated by the use of a barrel bedding V-Block and even then it is really not needed.
Good Shooting!!
Kirby Allen(50)