IMHO
Talking about my experience, when I flew light twins (some of them) I started the left engine first when there were daylight and I started the right first when it was dark, because in the nights I couldn’t see prop when it kicked and start playing with the levers, so I had to do it by hear. I preferred to do that because when you start the right first, the passengers used to get scared faster.
When I flew B727 as a F/O, we started 1,2,3 or 3,2,1 depending on the mood, unless we where pushed back with a turn, so we started first the engine inside the turn to help the tug, especially on rainy days.
Now, on the ATR I started the Nº 2 first because it has the prop brake, so it is like starting the APU, nevertheless I (SOP) do not release the prop brake until Nº 1 is stabilized.