Answer One: Ground coffee doesn't like the freezer or the fridge.
It's best to keep pre-ground coffee closed tight with a clip, and to store it in a drawer or cupboard. Try to keep oxygen away from it (you can keep the bag in an airtight jar for example), and try to finish it within a month.
Answer Two: Whole bean coffee kind of likes the freezer (if you do it right).
Freezing is actually a great way to fend off staling, if you do it right. Freezing food is so effective because the freezer’s extreme cold is great at killing the bacteria and mold that cause food and its flavor to decay. The issue with coffee then is keeping the beans dry. Moisture is the enemy of fresh coffee, so you need to do the following:
Place the coffee in an air-tight bag, press out the air, and place the first bag inside yet another tightly closed bag.
Store your beans in small quantities (you decide how small – enough for a day, a week, etc.) This part is important. When you take your frozen or very cold beans from the freezer, the warmer air outside the freezer will cause water to condense on the beans. This will damage the beans and cause them to grind differently than usual.
To prevent this, you can put several smaller bags inside a tightly closed larger one. Then several hours before you need the coffee (like the night before), remove one of these smaller bags from the freezer to the kitchen counter and let it come to room temperature before you open the bag. Whatever coffee you don’t use, store as described in How should I store my coffee?
I hope this was helpful. Any questions? Don't be shy - I love your questions.