The box on the bottom could be a 4 x 8 with some sides on it , not really high but high enough to take what paddling and camping gear you would have in it.
As far as a cover a tarp tied over it would work for weather protection. Just have some tie downs on the outside ( or inside ) for a rope to cover the tarp by criss crossing it. I did that on the inside of mine but I used bungee cords of various lengths to hold things in place. Had an eye bolt every 12 inches. If the trailer is not fully loaded what ever is in there will slide around as you go down the road.
They could also be used for anything else you wanted to haul in there. To make it easier make the tailgate section removable. As far as that goes make the back rack removable in case you have to move some tall things in the trailer.
About the boats , the rack can be high enough to keep it out of the way and still put the boats on it. When taking a spare boat then mount it on top of the camping gear... a simple mounting area for it on the front and back of the box would work.
Dangermouse has the ideal set up for just boats and camping gear but you are looking for a general purpose trailer. What ever you decide on , you will be making changes to it as time goes by and you use it......