It's not what diameter is needed but what diameter you want to hand. 5/16" would be strong enough but brutal on the hands. 3/8" is as small as I care to tug on with any force and really prefer 7/16".
Get double braid dacron line like StaSet from New England
ropes. All the major manufacturers make a double braid that is good for sheets
of thumb I've heard for length is 1 1/2 time the boats length for a genoa
sheet. a non overlapping headsail can be shorter. If these sheets
are going to be dedicated to a roller furling
headsail consider buying
a line twice as long as an individual sheet and secure it to the sail using a brummel splice. If you didn't want the sheet to be permanently attached to the headsail, use a cow hitch. Both of these methods will not hang up on the lower shrouds and make tacking way easier than sheets tied on with a bowline. I wouldn't use spliced on shackles. They are a waste of money
and real head
clunkers when the sail is flogging.