I was going to mention the 'Primer thing' but Rick beat me to it.
Anyways, using a Primer/Sealer does wonders, especially 1) if the ceiling was never painted before, or 2) the paint you want to use now is LIGHTER than the paint that's there. The Primer/Sealer prevents the current finish from 'bleeding through' to your new topcoat. Also, plan on 2 coats of finish paint because, well ..., with all do respect, none of us are 'that good' unless we're pros. (You won't use as much paint the 2nd time as you did the first time.)
Also, how 'hot' is it up there? If it's warm, let the heat out (or turn the heat down.) If the paint dries too fast, you'll see your 'W', and so on. And lastly, stick to using LATEX Primer/Sealer. Oil-based paint isn't necessary for the LR or DR unless you BBQ in there (or have a SPA in there.) As for 'washing the walls', I'd at least DRY-mop it to remove spider webs and such. (I don't think your kids walk or crawl on the ceiling too much, eh?) You can go heavy with the Primer/Sealer, and you can do 2 coats if you like.
Lastly, visit your local Paint Retailer (found in the YELLOW PAGES under PAINT - RETAIL.) I, too, spend good $$$ on good paint because it's always worked 'better' for me. (Others will disagree but for the few $$$ difference in price, I have the $$$ and feel it's $$$ well spent.)
Good luck! My best to ya and hope this helps.
Jay J -Moderator
PS: Measure the area you're painting so the Retailer will know how much to give you. Th Sherwin-Williams, MAB, Benjamine-Moore, Finneran and Haley, and all the other Retail Paint Stores have to be doing SOMETHING right with the fierce competition of Sears and Home Depot and Lowes all around them. (This should be 'considered' in your decision as to where you should buy paint ...)