Remove and drywall. Will save you a lot of pain.

It depends what you like. If you like the wood and want to keep there are options on keeping it and having it stained again. Figure out what you are looking for in the room and then go from there. From there, you have options based on what you are looking to do.

Cost wise, painting is by far the less expense and work. The painted boards could be given added interest by applying a light glaze over the paint.

If you go the drywall route, you might want to pull off a couple boards and see what is under it. If you are lucky, there might already be drywall under it. Some locales required this for fire code reasons.