PPG's Pure Performance is one of my favorites. Used it my own home. I like the eggshell finish. Link to 25% coupon: https://www.ppgpaints.com/diy/paint-coupon 

Link to product: https://www.ppgpaints.com/products/interior-paint/pure-performance-interior-latex

If the ceiling is really dirty, those studs will show like that. It is possible, than any paint would work, as long as you use a good sealing type primer, and two coats of paint. The reason for the sealing primer is because of the texture of your ceiling, other than vacuuming it, you cant really clean it well before painting.

I would use Zinsser BIN vs 123 primer.

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I always paint ceilings in a flat finish and this is what most people use on ceilings. Flat on ceiling, eggshell on walls and satin on trim and doors.

On a tight budget you can get good paint without going top of the line. Consumer reports tested all of the following with a 5 rating for hiding and resisting stains. . .