I LOVE string or mohair girths. I haven't found a horse who isn't comfortable in one, including ones that get rubs or irritation form every other kind known to man. In general, you size them the same as any other girth OR one size larger because they do sometimes shrink when you wash them. I always use a string girth for schooling and if you can get a brown one that matches your saddle, they are great for show.
Not having the elastic prevents being able to over-tighten them-many, many people over-tighten elastic girths. Simply because they CAN go up all those extra holes doesn't mean they SHOULD. I also love when I can find a good used balding girth. A single elastic shaped leather girth would be my next choice.
I'm not a fan of neoprene or fleece (especially those fluffy fake fleece) girths with double elastic ends. IME they are slippery and the saddle can roll, even if they are tight (not to mention they can be overtightened even more with double ends. Plus neoprene gets SO sweaty underneath and I've had more than one horse lose hair from the smooth neoprene. The Wintec neoprene, I find, is a little better.
I agree with those fluffy fake w/ double elastic. Oh how I hate those. I personally really like the Ovation neoprine. I ride in synthetic saddles (Wintec or Thorowgood) and prefer synthetic to go with them. These are shaped and very soft. Even my daughter's highly sensitive pony does fantastic in them. Plus, they're inexpensive which is always a huge perk. But that's now why I use them. I do because they work fantastic for me and my horses.
I find the double-elastic fluffy girths to be quite useful for sensitive horses. DD's mare is girthy in anything else. We do have a shaped leather for shows, but washed clean the others look pretty good too.