Spin halyard- if you are going 3/16 look at spyder line. Taperable low/non stretch. Warpspeed 1/4 would work also. Could also do apex 3/16 but a little stretchier than the other options. Some of the other new england rope products would work also.
Mainsheet- I really like the Marlow D2 I use (and did two other boats with the same) but I don't think they make it anymore. Warpspeed or endurabraid would work also. 5/16 at least. Both are taperable. I would stay away from vectran core stuff if you are going to taper it.