I too am not a professional, but I have Sheetrocked 2 houses and a 1800 sqft shop so I've learned a few things here and there.
Tape or Mesh? Tape, I tried the mesh, but get better results with paper
No don't try to sand then tape, you'll just tear up the paper. for the **** joints feather the seam out wider say 1 foot on either side of seam.
If you get good you can use fast setting compound and do steps an hour apart or so, the compound chemically sets and doesn't have to "dry" to be cured. It is sometimes called hot mud, and is available in 30, 60 and 90 minute working times. Tried these too - I'm not that good yet - they do allow faster turn around, they will not redissolve when wet, but they sand a bit harder. I only use them in high moisture areas like around tubs as again once dry they don't re-dissolve when wet.
Use a 6" drywall/putty knife and Taping compound, lightweight or regular, to tape all joints and first cover over screw/nail heads as the taping compound dries it shrinks a little and really ***** tape down tight. Then once dry use 6" knife to scrape down all the joints again to remove ridges and nibs of compound or high spots or a light sanding, or just use a wet grout sponge to re-wet the high spots and spread them out.
Next use a 12" knife to run Topping compound, lightweight or regular, over all your joints and screw or nail heads, note that when you buy compounds they are not necessarily ready to use, usually I add some water to thin it a bit so it spreads nice and even like soft butter on toast or whatever analogy you want... Once this dries knock down any ridges or high spots again then do Topping compound with the 12" knife on both sides of seams, so your joint is blended over about 22-24" of space.
Also note that if you look down the working edge of a drywall knife it has a bow to it, use it with the concave side down against the joint that way it helps to feather edges better. For a garage most people just do the taping step, I did the taping and one pass with the 12" knife and topping compound then called it good.
Just a simple oscillating fan will help speed up your drying times, in cold damp weather though it doesn't help much. Good Luck.
Ron