Almost all our meals should be stored in the fridge.
Typically a meal will stay fresh in the fridge for 3-4 days. If you're storing something for longer, it should be stored in the freezer.
It's best to allow your food to cool completely before you cover and place in the fridge. If you've prepped a very large portion, make it easier to cool down quickly by dividing it into separate containers.
You don't need to buy special containers. If you already have containers for leftovers or lunches, use these. If they are plastic and they look like they've seen better days it's probably a good time to replace these. If you want to treat yourself to some new containers make sure they have a good seal to protect your food (and your bag if your taking food to work) from leaks.