I too haven't really given much consideration as to how I start my saws till reading the comments on this thread subsequent to the "comedic" video posted.
I occasionally use the saw on the ground method, but most times I place the rear handle between my legs, bracing the front handle with my right hand and pulling the rope with the left.
If "drop" starting, I hold the front handle with the right and pull the rope with the left. But I really don't "drop" the saw much if at all. I use the decomp and use a quick assertive pull on the rope.
When I'm up in the bucket my starting method is drastically different. When using a top handle I hold the rear handle with the right hand and pull the rope with the left, pretty straight forward. When using larger saws of the conventional, non-top handle design it's the same procedure only I lean over the edge of the bucket allowing my right arm that is holding the rear handle to hang straight down outside the bucket allowing the saw to hang with the bar pointed straight down. This makes it so I'm not supporting the weight of the saw in an uncomfortable and awkward manner, and it lets the weight of the saw work for me and not against me making a pull of the rope with the left hand easy and safe. Being that the whole saw is outside the bucket there is zero danger of contact between the spinning chain and any part of my body.
Just realized that despite my being a righty, I pretty much always pull the rope with the left.