I removed some very old wall paper a few years ago, then painted without problems. Just cultivate some long-term patience (multiple days) for this project. Take your time and go over your walls carefully - multiple times. Give the walls a full day to dry thoroughly in between washings. If there is adhesive left, you should be able to feel it - run your hands across the walls and pay attention. You can tell the difference between old plaster/drywall mud and adhesive. It may take multiple wall washings along with some broad-blade scraping, but the adhesive will eventually come off. Try Dr. Bronner's mixed with white vinegar. I'be also seen recipes for paper and adhesive removal that are a mixture of vinegar, fabric softener and hot water - do an internet search. I think I had to go over all the walls only twice after the paper came off. Once the walls are very dry, sand them lightly just to be sure. As a last resort (I didn't need to do this), hire someone to re-mud/re-size your walls before priming and painting. Good luck!

I would use Zinnser BIN which is a shellac based primer. It uses alcohol as the solvent so it smells strongly at first, but evaporates quickly. I have MCS and it works well for me. I top coat with Mythic paint and love the combination.