I find I can do pretty much everything with a hairy 16mm three strand and a nice 12mm double braid. The 16mm is easy to hand hold (especially good for tensioning/lifting light bits) and tolerates natural crotching and branch/trunk friction well. The 12mm is for proper rigging, lifting with Hobbs etc, run through pulleys and rings only. I used to think I needed a monstrously thick line to be the big rigging hero I am. I don't. I've never broken a 12mm and with clean systems and thoughtful rigging, I don't worry about doing so.
16mm double braid is heavier manipulating it up the tree. If you really are doing a lot of heavy negative rigging, yeah, you'd want 16/18/20mm double braid but I'd only get it out for the end of the climb anyway. You're low down the stem by the time you need that much stopping power. I don't even own one. I just use both ends of my 12mm.
I don't have strong opinions on pulleys besides being wary of the ones that open with a button push and have built in swivels (e.g. Rock Exotica Omni Block). I'm sure they're fine but I'd worry about accidental button pushing or breaking the swivel from crossloading or something. Worry distracts.
Rings are mint. If you're tight for money, buy rings first. I spliced some onto a scrap of three strand, which won't win you any kudos on instagram but they're cheap and mega handy.
Pulley/ring slings you're only going to set once so they might as well be beefy. I don't like the fancy choking or spliced pocket ones. You can't move them around with a rope threaded and you can't get them as snug as tying a deadeye how you want it. Same for ring/pulley/portawrap at the base.
In terms of my own gear, I went straight from pikey tricks (branch/trunk wraps etc) to a Hobbs but I would often say to people I was climbing for to use whatever base friction they wanted or had on hand. Portawraps work and I can't recall one ever going wrong. They sit how they want to sit and work. Fixed bollards can tilt if not strapped tight enough and you can end up with a pinched rope and a piece you can't get down. Portawraps can also be tied/chained/shackled to things like machines/trucks that might have sharp metal edges and won't have the nice tree trunk shape a bollard wants to be strappped to.
One of the most important things is gloves for you and groundsmen. Leather, heavy enough to protect against three strand, light enough to operate biners and saws in. And bin them when they get holes in. You can't work confidently if you're trying to avoid a holey spot in a glove.
Curious what gear you used on your course btw? Pulleys/rings, double braid/three strand, portawrap/bollard/lifting bollard?