Since paper reacts as you described when it has absorbed water and dried, you need to seal up the wall first so the paper doesn't absorbe the water in the paint. If you're working in the bathroom or any other room with humidity, I suggest an oil based primer, followed by a mildew-resistant paint MEANT to go over the aforementioned primer (ask your paint retailer). If you're painting any other type of room, a latex primer meant to be put directly on wallpaper, followed by a latex top coat, will do the trick. I'm no expert but I put on 2 top coats of paint; not one. The pros can do it all with one top coat.
Before I sign off, I do want to say that prep work is the key to any final paint job looking great. If possible, use the sun's light to help show you any imperfections in the wall BEFORE you prime. Also, if your drywall is nailed, I'd screw in drywall screws (just a couple of inches from the nails), then either push the nails into the studs or remove them. This, of course, will require spackling and sanding (and priming). The thickness of your drywall will determine the proper length of your screws. And lastly, don't skimp on cheap paint. Even though I own stock in Home Depot I don't buy my paint there. I've always bought my paint at Finneran & Haley and spent $20-$28 per gallon. It really isn't that much more $$$ than Home Depot considering the alternative is having to look at a job that might have to be redone in a few years, plus, it just doesn't look 'creamy'. I'm just a little biased here. If you look at what the pros use (and DO ask them), you'll see that they don't use junk paint from Sears. They get the F&H paint (or from some other specialty store like F&H) at a lesser cost than I but they know the value of a good looking paint job. It's their livelyhood! If you want some good info on paint, go to Ask Dr. Paint. Take some time to peruse the site.
My best to ya and hope this helps. (I hope my $.02 isn't too overwhelming.)