New England Sta set is adequate line, although there is an extra charge for solid colors, which I prefer for a mainsheet application. (solid colors show less wear and dirt) Also the "hand" is average, at best.
I much prefer Samson Trophy Braid.... it is very comfortable in hand and grips the winch better than Sta-Set. No extra charge for solid colors.
http://www.apsltd.com/c-1504-trophy-braid-samson.aspx
On a 37 foot boat, with club race level line I'd go with 7/16" minimum size... Higher tech line would allow you to down size.. but you're talking big bucks...in any event your mainsheet blocks will determine maximum size. Again, on a 37 foot cruiser/casual racer... 3/8" is too small... All cordage manufacturer sites, and rigging service sites, will provide a size selection chart for all applications.
Oh..... Sta-Set X....absolutely not. That stuff sucks...it is stiff, very difficult to splice, and shows dirt in a heartbeat.... I hear they have solid colors now, because for years in only came in white with red flecks....... but the nature of the line is still the same. I built a halyard with the stuff years ago and could not wait to get rid of it..
Go with Samson Trophy Braid...you won't be sorry.