I'm fairly ambidexterous (sp?) with the trimmer. One thing the poll fails to ask is "left to right" or "right to left" Because forwards or backwards is only half of the options.
For general weekly trimming I always trim left to right, throttle in my right hand, left hand on the handle, walking forwards. Yes, this is technically incorrect, in theory... BUT, try holding the trimmer the other way, left hand on the throttle, holding it to your other side. Notice something HOT right against your hip? Yes, that's the muffler and exhaust. While they claim they were intended to be ran this way the engine is set up backwards to allow this to be done comfortably.
I'll walk backwards, basically pulling the trimmer head as I walk to knock down heavier growth. It's actually faster and when the grass is tall and thick this lets the trimmer kick out the grass into the lawn. Edging I just go whatever way works for the paticular area.
What it boils down to is there's no right or wrong IMO, do whatever gives you the quality of results you are looking for. I've tried holding the trimmer the other way and I have poor control of it and it's uncomfortable on my back.