I wouldn't use Spic-n-Span myself, any foo-foo cleaner could leave a residue that keeps the paint from sticking. Unless your walls are greasy or something (being the kitchen and all) I wouldn't bother washing them. If you feel you need to get the crud off though I would stick to something like ammonia or white vinegar.
Do you have stains? Shellac based primer is the absolute best thing there is for blocking things like smoke, tannin, etc stains those things just laugh at water based paints and will work their way though in no time. Working with it sucks, but it will stick to anything and block any stain I have ever seen. I just use it for spot covering because as I said working with it sucks, it is hard to get a good smooth surface when doing a big area.
https://www.rustoleum.com/product-c...sser/primer-sealers/b-i-n-shellac-base-primer