How to cover a popcorn ceiling (also has a basketball hole) with wood?

I would scrape off all the popcorn first. I would make a repair with a piece of sheet rock and joint compound over that hole as well. I purchased some primed ship lap from Home Depot to put on my bedroom ceiling. I located and marked the studs first and then ran the ship lap perpendicular to the studs. It went up easily and I used a nail gun with the right size nails to secure it into my studs. I see you have crown molding similar to what I have. I did not remove the molding--the ship lap butted up to it nicely--but that is a choice you need to make. I could have pulled it down and reused it over the ship lap or bought new but it didn't need to come down. If you do remove the crown molding the ship lap will look much nicer if you run some form of molding around the room. I cut my material with a chop/miter saw. I filled the nail holes, sanded and then painted using a brush to do the lines between the boards and then a roller. Bead board or pine ceiling strips would work as well but I found that this ship lap was the easiest to install. It comes in different lengths-8, 10, 12 feet so purchased the length that spanned the whole length of my ceiling so I didn't need to butt pieces together.

They sell beadboard in 4x8 sheets (like plywood its actually called "Plybead") that would be much less expensive and also less labor intensive than pine boards. First thing's first, you MUST find your studs, with a helper you can then use a chalk line to snap a line down each stud so you know where you're screws need to go.

I put up Plybead throughout all of the ceilings in my home and would recommend it. We used brad nails but after a few small places sagging a little I would encourage the use of screws as well as glue.

Beadboard is lightweight and cheap. I did a bathroom ceiling with it because of damage from a leak above. You can put it right over the popcorn IF you can locate the joists. You'll need to screw the beadboard into the joists. Cover the screws with nail polish! It colors it the same as your wood so they don't show.

Consider using a foam or pvc beadboard. They are extremely lightweight and are molded to resemble beadboard. No one can tell the difference. Screw the panels up. If you want a wood tone, using a painting technique to resemble wood is also possible. Good luck.

Depending on what ceiling you install, you may need to remove the popcorn. Many popcorn ceilings contain asbestos, especially pre 1980s. So cover the floor with plastic and wear eye and mouth protection. Work the drywall wet so you don't get dust on everything. Roll the plastic up with the debris and dispose of it.

You can add furring strips over the popcorn to level out the ceiling, and put them as close as 12" on center for ceiling tiles. Which for years was the way to go. They have some products for beades ceilings that are 1/4" x 3 1/2" and tack up nicely even or a novice.

I would be sure to patch the drywall because it does make a fire barrier.