Berries can easily be stored in a refridgerator for up to 3 days from picking. They can be stored in their original packaging or punnets; but in my experience I find that if you space them out a bit more then they tend to last longer. Never, ever, upon pain of death prepare berries before storing them. As soon as you break the skin of the berry it will start to soften and lose structure.
You can always freeze berries; but please please do not just shove the punnet in the freezer. When you defrost and then attempt to use you end up with a whole ‘brick’ of fruit. Use this method called ‘open-freeze’ to ready your fruit for the freezer.