I've bought all my gold and silver from T B Hagstoz in Philadelphia, PA.
I've delt with them for over 35yrs.
http://www.hagstoz.com/Order by karat, diameter, length.
They catalog and sell their wire in B&S gauge sizes. I don't know if that's a common in the industry or not.
Click on the 'conversions' link on their home page and it'll give the diameter in .000" (& m/m.etc).
(They have wire in different shapes too,,, oval, square, triangular, 1/2 oval or round, ect.
They'll anneal the wire if you want no charge before shipped,,I usually anneal it before use anyway again.
Metals available in sheet stock too.
I've always stocked 20, 24, 26, 28 & 30ga 24K round wire for my work. Some green and red gold wire too (18k) as well as well as a bit of 14 & 18k yellow gold wire.
20ga is about .030"
30ga is about .010"
For inlaying lettering numbers, signitures, etc,,I'd stick with 24k. Plus it won't tarnish like an alloy gold.
Call them (800#) to place an order, tell them how many inches (or feet!) of what karat gold (round) wire and of what diameter you need.
They'll tell you the price, shipping and you can put it on a card.
The gold is sold by the pennyweight (Dwt) and the more you buy, the better price you get. They usually tell me if I'm right on the edge of getting a better price if I buy a bit more of one dia or another.
It's worked for me for a long time.
What you'll need as far as diameter of wire depends on the width and depth of the lines you cut. You may need a couple or even 3 different diameters in doing some script lettering as the lines increase and decrease in thickness naturally.
Doing lettering like block where the lines are the same thickness, you can do the entire layout with one dia wire. The work goes fairly fast in those instances as you're not constantly changing wire sizes.
One inch of wire will generally inlay about 1 1/4 to 1 1/2" of cut line,,assuming a line of non-varying width like a border. It need not be overly deep. That just eats gold wire ($).
The excess gold will swedge forward as it sets into the dovetail and teeth that you made to hold it.
You want a minimum yet some excess on the surface to avoid tapping on the steel with your setting punch.
If you run into a line that is wider than the gold wire you are setting, you generally cut and start setting a larger dia wire for that area. Make a clean butt joint w/no overlap and it will go un-noticed when polished off.
One trick to span a relatively short piece of line with a bulge in it's width w/o using a separate piece of wire is to jump the 'gap.
Set the wire up to the wide area, skip it leaving the small loop in the wire that naturally occurs as you set it along a line. That'll be the extra gold to fill the space.
Now jump to the other side of the pesky wide width in the line and set the wire again to keep it from moving. You now have an excess of gold wire in the form of a little loop or hump over the space to be filled.
Carefully guide that wire down into the space with your setting punch and lock it into place.
The soft 24k will swedge together and fill the void w/o having to splice in an extra piece of larger dia wire.
Doing the operation is almost a nonstop action in setting the wire once you learn it, does away with the splicing in of a separate piece into the line with it's a joints and the handling of the tiny pieces of gold. That can be very time consuming.