Quarter-inch will kill your hands. I'd go half-inch, and in really light air you could use something smaller. Mostly you're tying the sheets on anyway, so you can have two sizes, with one as a spare.
I don't have an opinion on floating or non. If the sheets are getting in the water, the kite isn't flying well anyway.
Out of curiosity, are you talking about a bow-mounted assymmetrical one, or old-school with a pole?