Q: What tools/stuff do I need to skim coat?
A: Some prefer to put joint compound in a ‘mud pan’ (like a bread-making pan), and use what is called a broad knife, which is a wide putty knife. Beyond a 3 inch putty knife, you pretty much start calling them broadknives. I like to use a 10 inch one. it is wide enough. Too wide a knife and you wind up with a weird flex in the blade that can leave hump and ridges in your mud at overlap points.
Others will use what is called a ‘hawk’ (which is a flatboard ontop of a short stick, and then use a trowel with it (like what you use for cement). IMO, the hawk and trowel is good for ceilings as you can catch slobber that falls, towards your face for one thing.
For walls, I like the feel of the control I get using a broadknife vertically on the wall. Something about grabbing the handle of the trowel and pulling sideways bothers me.
So get yourself a 5 gallon pail of ‘lightweight’ ready mix joint compound. It sands easier. Too bad for you, trying to learn mudding by skim coating an entire wall is not easy for the first time. Mudding is like learning how to ride a bike – the training wheels thing, etc. The idea is so you don’t have to sand a ton of mud back off! Unfortunately, you can bet on you are going to have to do a lot of sanding.
Therefore you also need a sanding pole and sanding screen and/or those sanding sponge blocks. I love those things. They come in different grits. Get them all.
You also might consider getting one of those halogen floodlights that you can sit on the floor that adjusts, and has like a 300 watt skinny lamp bulb in it. As you mud, and especially as you sand, you want to cast the light on the wall at an acute angle so that you can see any waves, high spots, low spots, gouges, etc.