I normally just apply a coat of wallpaper paste and then run a scraper over it. If the water in the paste results in the paint being easy to remove then I am assured that any remaining paint is sound. It can be messy but it is cheap. the next day I lightly sand the wall and apply another coat of paste and hang the lining paper.
I do the wet on wet lining paper/paste because I am too lazy to use two buckets, one dilute, one full fat. I also find that one hot days I can be assured that if the paste on the paper has dried slightly, there is still wet paste on the wall.
I'd recommend using a roller to apply the paste to both the wall and paper. It is so much faster and easier to apply even coats. If you are working on old horse hair plaster walls it might be advisable to use a brush on the walls because of the risk of pulling out bits of grit. In those cases, I paste the wall, let the glue dry and then give it a light sand (to dislodge any grit) and then roll it and the paper. I also use a wide blade "knife" to smooth the paper and remove any air bubbles. One leaving site, I want the paper to look how it will when the glue has dried and shrunk back, another advantage is that when you apply the emulsion, you wont have any bubbles that look unsightly (even though they will shrink back).