How I store monofilament line
I store my line either still in the package spool or on the reel. Always in a cool dark dry place. I try to avoid storing my line were it can be exposed to the sun.
When you put monofilament line onto a reel, get the line as tight as possible. This will help to keep the line from digging in to the rest of the spool when have you that big fish on and it is fighting hard.
I like to keep my reels full of line. When a reel gets low on line they do not cast or retrieve as well compared to a full reel. Be careful not to overfill the reel.
I also think it is a good idea to wet your line before fishing. If you are in a boat you might want to let 50 or so yards of line out while you are going slow. Then reel it in as tight as you can.
If you are fishing from the bank then just cast a lead weight easy in to the water a few times and reel the line back on as tight as possible.