The general consensus here at TFP is that thinner covers are more cost effective and easier to handle. Thicker covers don't necessarily last any longer or preserve heat any better. The main purpose of a solar (bubble) cover is to not lose heat to evaporation and cooling at night. Clear or dark color covers likely add the most amount of heat from sunlight. However, the standard blue covers are a decent compromise and are cheaper than a clear or black cover.
Because I buy the cheapest solar cover I can (8 mil blue) I tend to ignore trying to protect it much from sunlight when it's off the pool... Not necessarily the best advice, but when my cover is rolled up, the reel goes next to the fence behind the diving board area. It's in full sun until about 5-6 pm, which is not great for the cover. If you can, put the reel in the shade when it's rolled up. Over the winter, it's best to wrap the cover (on the reel) in opaque plastic sheeting.