First I want to define the difference between a Carry method from a Ready method. A Ready can be expanded to a Ready To Shoot Position. These are used immediately before and during the fight and share one common attribute - that they either already have the muzzle on target, or allow the quick movement of the muzzle to a target once it has been identified.
These are what the bulk of the tactical shooting community are familiar with since they comprise the starting point for all the drills commonly done in a rifle class. But they require a focus and intensity that is short lived. For example, one cannot maintain a modern Contact ready, nor a traditional Low Ready for a five hour hike up a mountain.
Different in scope from a Ready To Shoot Position are Carry Methods (one cannot really call them
"positions" as one is usually on the move). Carry methods allow for moving the rifle from one point to another. In a military/tactical context, they are used for moving towards the general area of
where the fight might be. Notice I said "might be" and not "to the fight".
There is a subtle difference in anticipation, and apprehension. If I needed to cover five miles and I knew that at any moment, from any unspecified point, I may encounter an enemy, I would be using a much more "ready to shoot" method over a Carry Method, but it would be exhausting.
The Carry Method allows you to carry the rifle in the field, in situations where aggression is not
specifically expected. They allow for faster and freer movement that any sort of Ready To Shoot Positions.
First we have sling carry. I do not favor the so-called "American Sling Carry". That would be muzzle up on the primary shoulder. Common in the "sporting world" this interferes with the sidearm, and does not lend itself to a directional dismount sling-present to target. A relic of bygone times, we do not use it.
Instead we favor the African Sling Carry which involves muzzle down support side carry. This is very convenient in the field and allows for a quick dismount should it be required. If both hands are needed to climb the preferred sling carry is simply to sling across the back. This allows you to climb up a rock face, a building or anything you might need to do with both hands without needing to constantly manage a slipping sling and rifle. If wearing a ruck, the sling can simply be made longer.
If sling carry is not desirable, there are other options. These other options are rarely seen outside progressive schools as they usually do not have a reason to exist on the "traditional rifle range". But since we do a great deal of work in the AZ back country, we have found them to be quite useful.
First is Carry at the Balance. Simply find the balance of the rifle and grab it there. This works well
for running and for moving short distances in haste. The Elmer Fudd types will go apoplectic that the muzzle is not pointed to the ground. Well, I seriously do not care what they think. Carry at the balance can be seen anywhere light equipped men need to cover ground quickly. Reminiscent of carrying a spear, it is both natural and easy.
Every rifleman will have a preference, so try them all out and determine which one suits you, your
topography and your personal equipment best.