This has been one of my biggest problems too. The whole realm of storing fresh fruits and veggies. I don't know what to do come winter when even in sunny southern California there's is less or none of my favorite produce to choose from.
So far this is what is working for me. I don't wash my fruits and veggies until I'm ready to use/eat them. I store most fresh veggies in the fridge in zipper plastic baggies. Grapes also last longer in the zippered baggies in the fridge. The other fruits like peaches, nectarines, bananas, etc. I keep on the counter top until they get too ripe. I then cut them up and place them in freezer bags and store in freezer for smoothies. Bananas are great in the freezer. Peel them first.
I'm thinking of getting a seperate upright freezer to store lots of produce for the winter. I heard you can freeze Watermelon too. Anyone do that? I suppose it must work if you use it for smoothies, or juicing?