While you can buy and eat frozen mussels we feel that fresh live mussels are absolutely better tasting. If you have a go-to fishmonger then you should speak to him about the mussels and how to go about choosing mussels. They will tell you when the mussels came in and how to transport them home and how to store them.
When choosing live mussels make sure they have a tightly closed shell and then use your noise. They should have a nice briny, fresh smell to them. If you see a bag with a lot of cracked shells or a lot of the mussels has partially opened shells then those are not what you want.
Mussels are alive so they require you to store them correctly before you cook them. They have to get air so do not store them in airtight containers or plastic bags that will cut off the air supply and kill them. The easiest way is to put them in a bowl and then cover them with a tamp towel.
For a few days in the fridge put them in a colander and put that colander over a bowl and then add some ice to the top. When the ice slowly melts it can drain from the colander into the bowl keeping the mussels out of the water.