Great plan! One thing I would do is thoroughly clean the cabinets also, especially if you plan on using an acrylic latex primer. Hair spray is the enemy of water based products. Soap residue is also an enemy as it leaves an oily residue on the surface. TSP or Dirtex Powder are great pre paint cleaners. I don’t recommend oil based paint in high moisture areas. Oils will mildew faster than water based paints. Bull’s Eye 1-2-3 is one of the best primers on the market. It is labelled to bond to most surfaces without sanding (I would still lightly sand as you’ve already indicated. Better safe than sorry) and it is water based. Use a waterborne acrylic as a topcoat. Sherwin-Williams Pro Classic waterborne acrylic is an excellent product. Unless you have a major mildew or moisture problem existing, mildew resistant paint is overkill. Like I said, a high quality semigloss waterborne acrylic is not prone to mildew anyway.

Yep that’s the way to go! You can also buy small bottles of bronze or gold paint and hand paint the knobs and then clearcoat them with poly-urethene.

you have all the right ideas ! I would go with a bathroom paint that has an anti-mold agent in it. Its awful to paint with ( its like glue) but its worth it to not worry about mold and to not have to do it again if it does mold.
It is a few dollors more than regular paint.

i do this frequently in my business.

do not use Kilz.

use Zinsser brand Bin with the red label. it is SHELLAC based and will keep the tannins in the wood from beeding through.

then top coat with a high quality OIL based paint semi gloss.

spray painting the hardware would not be wise, as the hardware will get a lot of use and abuse. the paint will chip!

places like Home Depot, Lowes and Menards now sell many nice knobs and handles at very reasonable prices.

do it up right. you won’t regret it.