I was just watching this Trinity Squad Gaming report...

...and towards the end of the game there was a point when Rey was measuring range for a shot on Ventress. Measuring from the primary arc was range 2, but if measured from the closest point to closest point via the 360 arc, it was range 1.

In this case, should this be a range 2 primary arc shot or a range 1 360 arc shot? How do the rules apply in this situation? Can the player making the shot choose to use either the primary arc or the 360 arc?

First off: there is no 360 arc. Nobody has a 360 firing arc, but some attacks can be made outside of arc.

As for your actual question, no you don't choose which arc to use. If attacking with a turret weapon, the line of attack (for determining range and obstruction) is just closest point to closest point. You can't choose whether to use the turret ability.

Caveat: Sometimes you do still need to measure in arc, e.g. for determining whether Tactician goes off. In this case, without watching the video or knowing what crew Rey had, I'd guess what was happening was the Rey player was checking to see whether Ventress was in arc, to determine if Rey's reroll ability would be available.

So in this case...if closest point to closest point is inside range 1 (but this is measured from out of Reys arc), but the Ventress ship is simaltaneously in Reys front arc (even if the 'in front arc' measurement happens to be range 2...then Rey gets the range one 4 dice attack, and also gets to use her 'in arc' ability (as well as the Finn crew). Is this correct?

Yes, that's correct.

So in this case...if closest point to closest point is inside range 1 (but this is measured from out of Reys arc), but the Ventress ship is simaltaneously in Reys front arc (even if the 'in front arc' measurement happens to be range 2...then Rey gets the range one 4 dice attack, and also gets to use her 'in arc' ability (as well as the Finn crew). Is this correct?

That is correct, and if you watch the video you will hear the guys say that closest point to closest point is not range one so that is why they didn't roll the extra attack die and they only measured in arc to verify that the ship was indeed "in arc" to trigger both Rey's and Finns abilities. It definitely looked like it was range one on the screen but I did hear the commentators say it wasn't.