Use a good quality paint - I like Behr paint since it has a primer in it. Unless you are covering a dark color or something else unusual (like when I did a faux marble sponge thing back in the early 20's), you only need 1 coat of paint - no primer.
I don't think anyone mentioned this one - get a small hand-held bucket (mine uses disposable liners) for doing the brush work. Much easier than using the roller pan or directly out of the big can. Get the one with a handle you slide your hand into for ease in holding it.
Maybe something like this.
I have also used a roller on a stick that had a section to load paint into,
like this. My entry hall has 17ft high ceilings (it is 2 stories) so I needed to reach really high while on a ladder. It worked well and held quite a bit of paint (much more than a regular roller would). That said - if we ever repaint that area, I will pay someone to do it.