Serving mussels: Serve with dipping bread. Best is sourdough baguette sliced on the bias and lightly toasted - just enough so they aren't too crumbly and still have a little "chew". Serve "family style" in a big bowl with tongs, or serve in individual bowls. Have a ready supply of napkins, and a bowl for the shells.
Save the Leftovers! Do not throw it away any leftover broth! It is pure gold. It has a short shelf life, but if you ladle it (UNFILTERED!) into ziplock bags and squeeze out the air it will be fine in the freezer for months. I use it instead of water when making a packet of shrimp ramen. It. Is. Unbelievable. If you have leftover mussels, pop the meat out of the shells and freeze it for later use. Maybe for a mussel po' boy with a remoulade?
Buying mussels: Shop carefully, with an eye on quality as much as price. Before I stumbled on Costco mussels I'd had several less-than-satisfying experiences. In restaurants, they are stupid expensive for the tiny portions you are served - and often have a stronger flavor than I enjoy. Purchasing them fresh from seafood counters has also been expensive and with spotty quality. When I started seeing PEI (Prince Edward Island) farmed mussels at Costco in 5 lb bags for not much over $2/lb, I gave them a try. I'm hooked. They are extremely clean, high quality, and well-marked for freshness. Each bag is labeled with harvest date, wet stored date, packaged date, and sell-by date.
Storing mussels: Mussels should be alive when cooked. Once harvested the clock is ticking. They should be stored very chilled, with air circulating around them. They should not be submerged in water. Unless the store is only a few minutes from your house, I'd even have a cooler and ice waiting in your car while shopping. Perfect storage is in the refrigerator in a mesh bag placed in an open container with a mesh or drilled bottom that drains, placed in something to catch the liquid. Even better, the bag can be covered with crushed ice. This should give you a safe couple of days past the "sell by" date, max. But best is to delay buying them until as close as possible to when you plan to cook them. The fresher the better.
Prepping mussels: Inspect and clean them shortly before cooking - no more than a few hours before. It takes me about 15 minutes for 5 lbs. Rinse in cold running water, feeling for cracks (discard), checking whether it appears fully closed (if not tap on hard surface - if it doesn't close within 30 seconds discard). Pop off any barnacles using something dull like a spoon or a butter knife. You can also lightly scrub, though that is less necessary for farmed mussels. If there is a "beard" (visible ropy strands protruding from near the hinge), remove it. Best is to grab the mussel in one hand, grab the beard with your other hand using something like a paper towel so it doesn't slip, and sharply jerk downwards at a 90° angle to the "lips", resulting in a clean tear that does not much disturb the live mussel inside. Pulling it straight out will remove the portion in the shell that is connected to the muscle, which can be stressful on the mussel and some may not survive as long. That is ok if you are cooking immediately.
One optional tweak I have not yet tried, but know is well-loved in many mussel recipes: substitute heavy cream for the stock.