Need advice on taking off old wallpaper

So from trying to read how to do this I start with laying down a drop cloth, grab a perforator (wallpaper scoring tool) and scrape that on the wallpaper here. Then use a wallpaper remover spray and let it sit, and peel it off the wall/ use a paint scraper.

I’ve never done any of this before so I wanted to ask for some advice please. Also that ungodly red color I’ll try to cover with white paint (is that a good color for a bathroom or off white?) I’m planning on using this paint:

“HGTV HOME® by Sherwin-Williams Infinity Satin Ultra White Tintable Latex Interior Paint + Primer (1-Gallon)” because it states it can cover up any color. Is that true?

Thank you for reading and any advice you can offer. I hope you all have a great holiday :)

Btw I did not choose this bathroom color scheme, the previous owners did 😂.