mainsheets
any good "club race" quality line will be fine. New England, Yale, Samson, Marlow etc. all make great quality cordage. The most important thing is how the sheet runs through the blocks and how if feels in your hands. Your block system will limit line size selection.
I like the Samson Trophy Braid, it has the fuzzy feel... but I changed it out after a few years because it was getting stiff and not running through the blocks very well. I replaced it with solid color, black, New England Sta-Set because it was on sale at West Marine one weekend. Black because the mainsheet stays out side all the time and the solid color doesn't show dirt like the white stuff, and I went down one size to 5/16 because I wanted it to run freely.... which it does very nicely. I really like it....