Most wire wrappers will become tool junkies, the more tools you have the better. When starting into wire wrapping buy the best quality tools you can afford. Then as you replace or add more tools, buy the better quality tools, they make the work easier on your hands.
Remember all pliers need to be smooth jawed ( no serrations ). When getting a new pair of pliers check the edges for sharpness or nicks. They may need to be smooth or softened with a extra fine file or emery paper. The sharp edges could or may nick the wire when bending or shaping.
Wire Cutters come in all types, best pair for wire work is labeled flush or extra flush cutters. Most cutters are limited to the gauge of wire they are intended to cut without damage to cutters. Do Not cut paper clips or steel with them. Diagonal cutters will leave a wedge on both pieces of wire, which makes them harder to clean up to use.
Painters Tape, Automotive Detail Tape and more will be used to hold wire bundles together until the binding is done. I use Spring clamps in place of tape, spring clamps are also called drop ceiling clamps.
I glue leather in vices and vice grips to work with wire.