I truly think that your bench technique is far more important than either scopes or triggers. For un-supported shooting, such as field positions or off shooting sticks or bipod where you don't have a solid 3 point anchor for the rifle the trigger becomes far more important. Good optics and a target grade trigger will only help you wring out the last couple of tenths off the bench.
The groups with the 840 and the BRNO were shot with low power optics, max 4.5x and long heavy triggers. Being long and heavy they were predictable and broke consistently so off the bench it was pretty easy to be on the target when they broke.
You can shoot small groups with low power optics by not using the crosshairs for the aiming point but setting the bull into one of the quadrants bisected by the crosshairs and just touching the vertical and horizontal crosshairs which gives you a much finer aiming point than burying the bull behind the crosshairs. That's why when you see groups I've shot with some of these low powered scopes the group will be in one of the quadrants around the bull.
Yes the very first shot is the most important, if my guns throw the first cold bore(not clean bore) considerably away from the rest of the group that tells me that there is a problem with the rifle that needs work.
All my combo gun groups are shot with cold bores because the barrels are connected and as one barrel heats up it will walk the group depending on the relation of the warm barrel to the cold barrel. I fire one shot and set the gun aside until the barrel is cool again before firing the second. The drilling has very thin barrels and is the worst offender but only having a single shot in the rifle it isn't a problem in the field as it always put the first one on the money. The BRNO has much heavier barrels and will put the first three in very close proximity before starting to walk.
The same 840 with a 3x scope at 100 yards, I shot the first group and to prove it wasn't a fluke fired the second group.
An old German drilling in 7x57R shooting factory PPV 139gr bullets. This is the first group fired from the gun after I built a set of claw mount rings to mount a Weaver K-1.5 (1.5x) scope close to the barrel to handle more like a DGR. 100 yards
