Beyond things like a bin for the actual vermicomposting, and a sifter like we discussed in harvesting, there are a few items that are handy to have, save time, or otherwise make life a little easier. Like a gardener, doctor, tradesperson, or artist, each of us will settle on the exact tools and methods that mesh with our process and routine. But here are some ideas for starters.
These are simply must-have equipment for many vermicomposters. I have a whole stack of them. We use them for mixing up bedding, harvesting vermicast, catching runoff, baiting out worms in harvested castings, sorting worms, curing and storing, on and on. I know of several large commercial operations that use hundreds of these exclusively for their bins. Most gardeners can think of a half-dozen or so uses as well. The ones that I use are 7-gallon and 16-gallon mixing trays that can be purchased inexpensively at big-box stores, usually in the concrete and/or drywall sections.
This is on the "optional" list but can be good to have, especially if you're a little icked out digging in compost. They can be nice if you get a batch of scraps that are getting gloopy, if your bin gets over-wet, or any other time that you don't care to get your hands into the action. I use mine for chasing down centipedes because I don't wear gloves. Rather than use the traditional trowel, which can cut and injure worms, we use a digging fork of some sort with tines instead of a broad blade. Safer but still, operate it gently! I love getting my hands into a living system just to keep dirt under my nails, and because tactile assessment is the best way to gauge moisture and texture.
There will be times especially here in Colorado that you'll need to up the moisture in the bin, sprinkle up some bedding or the like. Water in a stream like from a typical watering can will mostly just run through (and cause trouble in the bottom of your bin), so something with a "sprinkle" works much better. I also have a 2.5-gallon pump sprayer with a wand that gives a fine mist. It gets used all the time for plants and is also handy in the wormery, but it does take a while to put out larger amount of water.
There are lots of vermicomposters who use gloves every time they go in to the bin. I am personally not one of them, and while some vermicomposters make great sport of this practice I see no reason to be a jerk and shame them. To me personally most gardening or work gloves are a little too clumsy for worm work, which is why I think most glove folks use nitrile disposable gloves in their bins. I worked for decades in health care so I've filled my share of landfill with these gloves and I'm a little sensitive to the waste, but try with and without gloves and see what makes you the most comfortable.
As we discussed in optimizing, the more you can chop up and mix in your food scraps and living materials the more quickly they'll be available to the worms. And the fewer opportunities for odor or pests you leave available. Now full disclosure I'm a knife guy, so I drool over handsome traditional cutlery. But while I do nerd out on this I have found this system to be very convenient in the wormery. It has two parts:
An Ulu, and
A rubber feeder pan
The Ulu is a traditional utility knife from the First Nations people of Canada (and I believe Alaska). If you want to be seriously impressed, check out youtube for videos of people processing salmon with these things faster than you can put on a sock. As you can see, it's something along the lines of a cleaver but that is gripped above the spine, and has a curved blade. They are AMAZING for chopping since you are exerting all the force down through the material instead of out in front of your wrist, and they are good slicers and general utility blades as well. You don't need an expensive one for this, an $18 knockoff is perfect.
Then the farm tub is a tough, somewhat flexible rubber tub you can get at feed stores, farm supply or online. I like one that's about 16" across and 4" to 6" deep, the tall/deep ones can be a little more awkward to chop down into. These are so great because they're waterproof but also can stand up to endless chopping and abuse, and being flexible makes pouring out of them a little easier. They're also forgiving enough that they won't ruin your edge chopping into it week after week. These are another item that ends up being used a lot around the house once you have one.
Shredding the bedding. It is one of those meditative tasks that all home vermicomposters develop our own rhythms and preferences about. You absolutely do not NEED a shredder: hand-shredding is a time-tested, honored tradition that... well, that I gave up pretty quickly to be honest! Since corrugated cardboard is available everywhere and such perfect bedding material, getting a shredder that can process it can be a welcome addition. I have an old 16-sheet office shredder I dumpster-dove that eats cardboard all day without a hiccup. If you go the shredder route I would recommend one rated for at least 12 sheets, but 16 is kind of entry-level burliness for processing cardboard.
Buckets are another hundred-uses doodad. Use for storing finished vermicompost/bedding/food scraps, soaking bedding to rip up or hydrate before adding, for mixing things, or for a seat when you need a minute off your feet. They even make a backup worm bin or breeder setup! They stack well whether full or empty. But be aware that different buckets have slightly different dimensions, so I try to stick with one when I can and buy 4 or 5 with lids when I'm at a hardware store. I personally get the dark blue Lowe's buckets as they are light-proof and inexpensive.
And while we're on buckets we have to mention those sifters that I use. There are many ways to sift vermicast and I've built several different models, but I keep returning to these "rectifiers" that sit in a 5-gallon bucket. While you certainly don't have to use the bucket, a bucket catches all the sifted material which makes for much less cleanup. Also if you're doing this for a few hours, the weight of supporting all that material adds up! So if the bucket carries the weight and you're just rocking it back and forth, from an ergonomic (that is, "lazy person") standpoint it definitely does save you some Wheaties.
Whether purchased in a rectifier or making your own, the universal all-purpose nuclear bedtime story screening material is called "hardware cloth". It's a galvanized mesh wire that is referred to by the gap space between wires. One-quarter-inch is typical for vermicast screening use. One-eighth inch is finer obviously and makes for a really gorgeous sift. I also have a half-inch one for regular/bulk compost, fine mulches, or super-coarse screen jobs, and a finer one for cocoon sifting.