Use wallpaper paste remover to be sure you have all the glue off. You can use the kind you mix with water. It works very well. You might have repairs to do. And you may have to lightly sand the walls to be sure they are smooth. If you do repairs with spackling or joint compound, you will want to primer those spots first. If existing wallcolor is very dark and you want to paint a light color, be sure to primer entire wall and you can tint primer with some of the wall color so you don't have to put so many cover coats on it. Good luck.
Wash the walls with Wallpaper remover or fabric softner then wash again with tsp and well rince. Let it all dry and do your repairs ( if not to big of holes then lite spackle will do). Then sand the spackle areas and prime these spots ( if there is a over abundance of repairs then prime the whole wall). Yes you can tint the prime to 1/4 strengh ( we call this 1/4 formula of the desired color). Now with 150 -180- grit sandpaper sand all the walls down litely and your off to the races.
When ever I strip wallpaper and than want to paint I always prime the entire walls with bulls eye 123 made by zinser. Even though you wash the walls there could still be paste residue left behind. This can cause your paint to crack. Every paper that you remove is different.Some have a very heavy paste. Years ago I would always prime with oil to seal off the residue but today I find the bulls eye to work great. This primer can be tinted.