All else being equal, I tend to start on the left, but there are factors that can change that. For example, if by starting on the right I can end pointing in a direction more conducive for the next task or if the right target is significantly larger than the left so I can get on target for my first shot faster or if it is a sweep where you hit the starting target more times than the others and the one on the right is larger.
I sometimes do shoot the rifle and pistol from opposite directions - I think I did that on one stage this month and I had a logical reason for it that I don't remember now.
Shooting traditional, I always shoot my right pistol first, but when I was shooting gunfighter, I forced myself to mix it up because "left first" was becoming ingrained and there are often situations where it is much better to start with the right one.
AM