fascia and drip edge
You will need more than 4 inches for a gutter , so you will have to go to 1x8 facia.If you are completely reroofing why not just use the existing 2x6 as a sub facia and apply 1 by facia over it, unless it is rotten.If i understand your description. the "end rafter" boards you refer to are the ones running up the gable ends of the roof, and they are called "barge" rafters locally, but I think that is a corruption of the term verge or varge rafters.Most local roofers do not install a drip edge at the bottom of the roof, only up the gables. They leave the shingles about an inch long so they can hang into the gutters for better water flow, but there is quite a difference in rain from Phoenix to New Orleans. I'd go with the local installation practices.