Peppers do best at a temperature of about 50 degrees F with high humidity. Most kitchens do not have storage space to accommodate these requirements.
Your best bet is to put peppers in a paper bag placed in the crisper drawer of the fridge. Plan to keep them no more than four or five days.
However, the same peppers that have no natural resting place in the refrigerator, do amazingly well in the freezer. Dice a raw pepper, place it in an airtight freezer bag, put it in the freezer. Small hot peppers may be left whole. After a brief thawing, they can then be cut and seeded.
Peppers will lose crispness once frozen, but will still be good for cooking and stir fry. Peppers may be frozen for six to eight months. However, hot peppers will lose much of their heat over time.