Ready-mix all-purpose joint compound is the default. It comes in a 4.5 gallon 63.7 pound pail, shrinks a little, sands easily, and forgives a bad day. It is what the calculator numbers are built on. The thing it cannot do is cure fast. Three coats of all-purpose is a three-day job at a minimum because each coat needs to dry overnight.
Setting-type compound (hot mud) fixes that. It comes in bags labeled 20, 45, or 90 minutes. Those are working times: how long before it starts to chemically set. Hot mud is harder than ready-mix, sands worse, but lets you do three coats in a day on a small repair. Use it for patches and for the first coat under paper tape on a butt joint.
Paper tape versus mesh is the other constant question. Paper tape is stronger and stays stronger. Mesh is self-adhesive and easier to put up solo, but it has to be used with setting compound, not ready-mix, because mesh flexes and ready-mix cracks over flex. Mesh on butt joints with all-purpose mud is the fastest way to get a crack in six months.
Screws: 1-1/4 inch coarse thread #6 for wood framing, fine thread for metal. Long enough to bite the stud, not so long they blow through. Nails are out; they pop as the framing dries and leave a lifetime of drywall dimples. Spacing per GA-216 is 12 inches on center on ceilings, 16 inches on center on walls, with perimeter fasteners within 3/8 inch of the edge.
Outside corners get metal, vinyl, or paper-faced bead. Vinyl is cheap, forgiving, and cuts with a utility knife. Paper-faced is the finish-quality choice. Metal is the old standard and still works if you do not dent it during the hang. Inside corners get paper tape, not bead.