I am drywalling the house bathroom, I using 1/2 green board,
What type of joint compound should i use? The one with green lid or the blue
lid, what is the difference? Should I use paper tape or mesh tape?
Sanding? first use 80, then 240 and apply 3 coats of mud?

Eww im not sure i would wanna use 80 grit on drywall. Most peeps i know that do it use 240 screen for sanding and they usually only have to knock nibs off. The key is to put the mud on slick where ya don't have to sand much if any at all...

I have had better luck with paper tape than mesh, but mesh is supposed to be stronger. Paper is sure a lot easier to work with and being thinner makes a nicer joint IMHO.

240 grit is the coarsest grit I have used, I finish with 400 and prime. Two top coats and your done.

I am a remodeling contractor(sorry) and I always use the lightweight compound. You should thin it from the bucket with water, it will be easier to spread. Paper tape is what all pros here in my area use. I have used both but now only use paper. I make up to 4 passes on my mud, all real thin, dries faster and is smoother, requiring less sanding. If you are installing tile over the green board then 2 passes are fine, just enough to form a monolithic substrate that resists movement. sand with medium or fine "screen". Both are fine w/medium dont press as hard, fine requires more effort to smooth area. Just dont leave sanding marks in mud. The new "dustless" mud really gums up sanding screens and is not really dustless. have spackeling compound ready for spot fixing during painting. paint one coat of good primer. two topcoats of color. darker colors show mud mistakes more than lighter colors.