I use a set of old guitar strings I got from the kid down the street. Six different thicknesses,
Note that when a smooth wire is or gets too slick to get enough friction for a good burn simply use small piece of sandpaper to rough it up, maybe 320 or 220. Pinch and pull the wire through, turn the wire a bit and repeat.
The best burning wire I ever found is thin galvanized steel lockout-tagout wire,
used decades ago to fasten safety and info tags to industrial valves and switches and such.

(Live life to the fullest. Turn nice handles for your friction burn wires!

These wires make clean, fine lines.
I don't like fat burn lines on the kinds of things I make, especially tiny boxes like these needle cases/pill boxes.

JKJ