Once cooked, 3-4 hours refrigerated should be fine.
As for the cooking, America's Test Kitchen directions...simply amazing results. As good or better than any muscles I've ever had, ever, and I love the things, try them every chance I get. I don't remember the directions offhand, but it involves a hot oven, doesn't take much time, and the texture of the muscles is fucking fabulous.
Also, look for farmed mussels that are wet-something...I'm inclined to say finished, but not sure that's the right word. Basically, it means the mussels were harvested then put in tanks with clean water for a couple of days before processing...this results in grit-free muscles, and it's worth looking around for if you can get them. I rarely find them anymore. Farmed muscles taste just as good as wild and are generally bigger and healthier.