Going to have cut out all that old tape and loose paper first.
Make sure to check out how thick that sheet rock is, it should be 5/8.
Going to need two rows of tape.
I'd use a 6" knife to set the tape, 8" for the second layer, then finish with a 12".
No need to lay it on thick, drywall compound is to just fill in the low spots.
If this is done right there should be no need for sanding until the last coat, you just knock off any high areas with the drywall knife before applying the next coat.
Make sure to wipe off that whole area before priming to get the dust off.
It needs to be primed with a real primer, not paint and primer in one!
I'd do the finish painting with a 1" nap roller for a better chance of matching that stipple you have on the ceiling.
It will need 2 coats of finish paint.
