There are many different jewelry-making styles and although each requires several tools that are similar, many techniques need specific tools. Let's look at a few options to help create your Ultimate Tool List.
First: A pair of crimping pliers, most often used by beaders, can also be used by wire wrappers to tuck the end wire in on a wrapped loop. Chain maille artists often use two pairs of wider tip chain nose pliers. One pair is sufficient for a wire wrapper, who also likes to have a pair of needle nose chain nose pliers to make tiny loops at the very ends of wire.
Secondly: Folks who do a lot of round wire designs use almost any pair of flat nose pliers, but wire wrappers who work mainly in square wire need a pair that have perfect angles (with no dips or bulges on their sides).
Some people like pliers that have extra cushion on their handles; others) think the extra bulk is difficult to hold for long periods of time. Then there is the choice of longer handles. I am a firm believer that all pliers need to have a good spring hinge of some sort, so you don't have to constantly open pliers while using them.
Just about everyone can use a nice set of fine diamond files and/or an Arkenstone to remove sharp ends and burrs (then again an emery board works well too, even on metal clays), and we all need a good pair of wire cutters as well as a pair of small nippers for tight spots.
Then there are mandrels. Almost all jewelry makers need a neck mandrel, a worthwhile investment! Depending on what style of bracelet you want to make, some folks like to use a steel bracelet mandrel. Most wire wrappers don't use one, as we often incorporate beads and stones into the design (that don't do well while forging on a steel mandrel). Most of us use plastic bottles and shape by hand.
Mandrels usually require that an item be beaten on it or forged, so a mallet is necessary. I like a medium had rawhide mallet, but lots of folks like using a nylon one.
Forging is used in lots of jewelry making styles, so a basic chasing hammer and bench block should be on your list too. And if you want to get into more metalsmithing, a dapping block will be useful along with a jeweler's saw and diamond blades.
If you are looking for universal but 'good' tools, on a scale of 1 to 3, 1 being best, here is my opinion on our tool sets:
3 - Starving Artist Tool Kit: Mostly for beaders, has essential tools, but will not hold up to most wire projects;
2 - Wire Jewelry Tool Kit: Very good for wirework beginners as well as for almost all jewelry making arenas;
1 - Premium Wire Jewelry Tool Kit: Better, tools have longer handles and good cutters, but the flat nose pliers are not square on all sides;
With this Ultimate Tool List, your workbench is ready to start creating wire-wrapping masterpieces.