The best, cleanest looking sinew strings are made from long backstrap tendons. Making them from leg tendons involves a lot of splicing and the fibers are often torn, frayed, etc. I like to split my strands as fine as possible for the strings. Backstrap fibers seem inherently finer than leg tendons, but that could be my imagination.
I prefer to do it dry because I have had bad experiences with stiffness and spiral winding after the strands glued themselves together and shrank while drying. It also develops this weird discoloration and kinda looks like it is rotting. It's hard to keep sinew clean and dry all the time. All my quivers have a compartment where I keep pure tree rosin, among other things... Any kind of rosin will do, but it needs to be hard rosin, like the kind violinists use. I religously rub my strings with rosin. It seems to keep the strings really clean from bacteria/mold. I don't use wax or any kind of adulterated tree pitch for sinew strings. They seem to moisturize them.
A lot of people moisten or wet their strings before twisting, but their strings all look like they were pulled out of a dumpster.
I never paid much attention to diameter for strength, because this stuff is just so unfathomably strong. Spliced areas may slip if it gets wet though. 1/8th of an inch is more than sufficient for a 150 pound horn bow in my experience.