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For jobs like yours I've had good luck with the B.I.N. shellac based primer. Brush, roll, or even the spray can works on small areas. I might be tempted to prime the whole ceiling, not just the repair areas. So roll it on. Probably buy the gallon.

The Behr ceiling white comes in 2 gallon buckets iirc. You don't need that much. Maybe you have more ceilings that you can paint!

Good luck with your project.

If you have brown water stains showing, you need either an oil or shellac based primer. Those brown stains are water soluble and will come right through even the so called "stain blocking" water based primers. An oil or shellac based primer will stop them dead. Primers such as Original Kilz or Cover Stain will dry in about 45 minutes and can then be painted over with any oil or water based finish paint.

The spot primed repaired area might possibly "flash" out, as it possibly will now be better sealed than the ceiling surrounding it. It using a dead flat ceiling paint, it probably will not, however, if using a higher sheen paint, spot prime the repaired area and plan on giving two coats to the whole ceiling a assure an even sheen overall.

Just buy a spray can of Kilz, BIN or CoverStain and spot treat the stained areas. A ceiling that size can probably be done with 1 gallon unless you are planning on two coats, then you might need 2.