Hi Ken, here's a great video to show you all the steps you might not think of at the beginning. You may want to use a special enamel paint. Prep is the most important part of the project! :)
I would use a roller on an extension paint stick.
I would get one of those edger brushes and paint around the top edges first, then use a roller on a stick and roll the paint on. I have had great luck with these rollers (although, they're a bit more of an 'investment': https://www.homeright.com/products/paint-rollers-edgers/
Make sure you get a paint that contains an additive for mildew resistance. If it's a re-paint, then dust (I use a Swiffer type) the surface. You will probably need a 2 step ladder rather than a traditional ladder since it's a small space. I recommend cutting in with the Wooster Shortcut 2" angled sash brush. It has a rubber handle and makes it so much easier for tight spaces. Once you have cut in about 3-4" at the edge of the area as well as around the light fixture, you can use a roller to paint the rest. I would advise getting the roller frame that extends. My favorite came from Home Depot (Lowe's doesn't carry it). It is compact enough for normal handle length but extends about 18". The handle is cushioned which is a must for me.
Make sure you use a paint with a flat finish!
Just use a roller with a long pole so you can reach and then use a brush to get the edges. Use painters tape to block off the walls.
Measure out from edge six inches. Paint from edge to line in preferred color. When dry, tape off one inch more. Paint inch a shade or two darker (add black, brown or other darkening color to original paint). Last paint center a few shades lighter, ( add white to original paint). This gives a raised look and feeling to ceiling.
Hi Ken, I used an alkyd base for the ceiling in an eggshell white, use an angle brush and cut in the edges and corners first, if you don't have a steady hand use frog tape to mask what you don't want painted. Use a roller for the rest. I have also attached some ideas for you to look at for small bathrooms, mix and match some of them. I use a step stool and an extendable roller
I used a paint roller with a long wooden pole screwed into the handle of the roller. Got the pole at the hardware store. I used painters tape around the top of the walls first.
Clean and repair your ceiling first. I couldn't believe all the dust that was up there! I tape and then cut in the wall/ceiling edge and roll the paint on while the edge is wet, using an extension pole with my roller. Good luck!
Bathrooms need to repel their high moisture condensation and you need a gloss paint.
I used to squeegee the ceiling in my master bath over the large shower area! Flat paint will not be squeegee-able.
You can roll your bathroom ceiling. Or if you cover everything you can spray it with upshot kilz
Here is the kilz . https://amzn.to/3bAkhX6