Everyone pretty much answered about how wet you get, so I'll tell you what I wear.
Yes, jean shorts will be very uncomfortable. So will cargo shorts. I usually wear some type of dri fit clothes. Basketball/mesh type shorts are the best to wear. Along with dri fit shirt. You can even find dri fit underwear. May sound silly, but I recommend them. I learned a lesson the hard way the first time we went. I was prepared the 2nd time around and was completely dry about an hour later. Might even consider taking a change of clothes for the end of the day, just in case you don't try off in time. DW and I did. We just rented a locker and kept them in there until the end of the day. Also took a hand towel along to help dry us off.