You didn't say how big the boat is, but I'd start with 3/8" as the minimum size for hand comfort, and go larger if the chute size demands. See http://www.neropes.com/LineSelector.aspx
for guidance on size. I'd use the basic Sta-Set line or equivalent. I've never heard of the use of floating line for sail control lines, maybe good for the dingy painter...the tapered line is great for racing applications where you'll pay 3 times as much per footfor low weight..shouldn't matter at all on your cruising boat..KISS.