I have a cabinet with sliding doors for my thread cones. It is narrow so can put only two cones deep but that is good as I buy two of each color(easier to work with). I put any bobbin with thread still on it inside the cone it belongs with and keep the cone and bobbin in the original bag the cone came in. I keep the bags from any empty cones in case I have one rip. My cones are all Superior thread company. I don't know if other brands have a big enough center hole to hold the large bobbin. I also stocked up on bobbins(like 35 I think) so I don't have a problem running out of bobbins though I have come close once or twice.
My cabinet is set on an southeast facing wall which has windows so it doesn't get sun at all as there are no other windows there(basement).