In the last few years I’ve begun to take the easy way out with excess peppers. I core them and throw them in a freezer bag and into the freezer they go. Done.
This works well if you need peppers for a cooked recipe. I remove them whole and cut them into quarters if I want to grill them, dice them for a mirepoix or other sauteing mixture – all while they’re still frozen. I do the same with hot peppers and sweet peppers.
Peppers are also good dehydrated. They’re fabulous for making pepper jelly and you can puree them (maybe with some garlic and/or onion) to keep on hand (frozen in small quantities) for adding to chilis, stews and spaghetti sauce.
If you’re planning to use yours fresh, refrigerate them unless you’re going to use them tomorrow. Lots of water in those pepper walls means they’ll start to wilt if just left on the countertop for too long. That said, I’ve had luck towards the end of the season (cooler weather) in keeping my peppers on the counter (and keeping an eye on them) and watching them turn from green to red (or whatever color that variety ripens to). Then if I still haven’t used them, they can go into the refrigerator in a ventilated plastic bag to keep for a little longer.