I think we don't have enough real information to guide you, to be honest. You have to run wires down or up within a stud bay either from the floor above or floor below, and then across the wall horizontally from the chosen bay to the left or right to the device box that you'd like to connect.
If you don't have a flexible auger bit for a drill that allows you to drill through multiple studs horizontally from a single access hole (or you have to drill through exterior studs where there is insulation that would get caught in the auger), then you will need to cut an opening in every stud bay.
Regardless of which size and shape of cutout you choose, whether it be a round hole or a square one, the most important thing is that the centre of the studs forms the edges of the hole. The reason for this is that when you re-attach the drywall, you will need solid structure to provide backing for the drywall.
There are ways of adding backing support to a hole that has no framing behind it, but it will add time and material cost to your work.
So, if you are cutting a rectangle between studs, make sure the sides of the rectangle fall on the stud centers. This means that you will probably hit drywall screws as you are cutting, but that's not a big deal.
If you are cutting a round hole, cut the centre of the hole on the centre of the studs so that you can re-attach the cutout in the centre.
What I have done in the past is cut rectangles that are 16" wide, because the studs are 16" O/C. When I have run new NM cable in interior walls with no insulation, I only need to cut the drywall at the top/bottom of the stud bay to pull the wire into the bay and then a hole at each end of the run. I use a flexible auger bit (48-72" long depending) to drill through the studs without removing excess drywall.
Keep in mind that auger bits will cause you some frustration in some cases. The bits can get dulled easily if you hit a nail, and they might need a fairly powerful drill to make it through older wood.