One of
these come in handy if you plan to use resources like
Steam Engine for calculating ohms. Drill bits and micro screwdrivers work fine, but the jigs give you a few things less to keep up with in your kit.
I've tried a few sets of ceramic tweezers, from cheap-o eBay specials to more expensive brands, and don't particularly care for them. I lifted a regular pair of tweezers from an old manicure kit that my wife no longer uses and pretty much use them exclusively for pinching coils. You probably have a similar pair sitting unused in a drawer somewhere.
A decent pair of micro wire cutters are a must. Tried using some nail clippers from the same manicure kit, they were rubbish. Get the wire cutters. Also have a sharp pair of scissors, the smaller ones work best in my experience.
For simple, no-nonsense coil builds, I personally recommend Kanthal A1. Gauge is dependent on the ohms you're shooting for; 24/26-30 should suffice for many simple builds. Venture out to more complex builds and different metals once you can build the simple coils comfortably and cleanly and understand the benefits and potential risks of temperature-dependent coils.
Wicking material is your preference. I've recently been enjoying unbleached Japanese cotton pads, but still have a few metric tons of organic cotton puffballs that I bought when I first began building. One unraveled ball can last multiple dual-coil builds if you're conservative with the stuff. I don't think I'll ever run out of the big pack I have, no matter how hard I try.
A digital voltage/ohm reader with 510 connection is useful if you don't trust the readings your mod gives you, assuming you own a mod that displays your ohms. I have an inexpensive digital eLeaf reader that I rarely use anymore.
Shop around and all of this can probably be had for less than many of the decent kits on the market. Plus you'll have a nearly unlimited supply of the finite items. Knowledge is the only item that won't come with any kit, but luckily for all of us it's abundant and free. Don't skimp out on that one if you decide to build your own.