My wife wants to wire wrap.

I would suggest getting her copper wire to start.  That way if she messes something up and has to start over, it's not costing as much money.  Once she knows she likes wire wrapping and wants to continue, she can move on to Sterling if she wants.  Lots of people like copper and it takes a nice patina if she chooses to go that route.

I prefer square wire for regular wrapping and round wire for weaving.  Square is easier to control (doesn't roll around while you're trying to shape it) and I actually like the looks of it in a finished piece better than round.  18, 20 and 22 gauge should allow her to wrap any size cab.  She will also need 21 or 22 gauge 1/2 round wire to use for binding wires.

If she would rather use all round, the same sizes would work.  You will need the 1/2 round either way.

She'll also need a variety of pliers and a flush cutter.

rockjunquie will chime in, I'm sure.  

Hi Brent, when your wife goes looking
for wire she will find things listed
as "half hard" and "dead soft" as well
as square, round and half round, as both
Robin and Tela have mentioned. In some
of the very informative tutorials pinned
in this section it mentions 22 gauge
square dead soft for the wraps and for the
bindings 21 guage 1/2 round 1/2 hard. I am a
wannabe wire wrapper and have only gotten
my feet wet, so I would certainly defer to
the experienced wrappers here.

If she were to join there is so much information
that would help with the learning curve.

Woops!  Yes we did.