"Best" is always a relative term. I normally rinse the coils with hot tap water immediately after removing it from the cooled wort. Then I hang it upside down over a floor drain to drain all the water out. I inspect it for chunks, tree leaves and bumblebee bodies and walk away. If for some reason it starts to develop a layer of something on it I will give it a short soak in StarSan or PBW (whatever I have mixed at that moment).
There are no issues, chemically, with leaving it in the whole boil. My chiller interferes with how the wort moves and may have a slight affect on hop utilization. Although that effect would be very small. It is mostly just a PITA to work around so I drop it in with the Irish Moss at 15 min.
Paul