Unless you are going to eat your oysters straight away, it’s better to buy them unopened. Given the proper care, oysters will live for 5-7 days after being harvested. You can keep live oysters in the fridge. To ensure maximum quality, put them under a wet cloth.
If you want to keep them in an eski, cover them with a damp cloth. Ideally, the esky should be about 4°c, but they’ll be fine even if it’s as warm as 10°c as long as you eat them within a day or two because even at 10°c they’ll remain alive and retain their delicious juice.
Once opened, oysters will keep for up to 7 days in the fridge, but be aware: they will absorb any strong flavours (for example rock melon and onion tend to taint the flavour, no matter how well packed your oysters are).
When buying live oysters, make sure the shells are firmly closed. Discard any that are open or appear to have lost their water. Clean the shells before shucking in order to avoid getting grit in the oyster and having to wash the meat (you lose the juices when you wash them!).