As far as gauge you should always get the correct gauge of wire for your application. Too thin and there is a risk for safety and fire.
Meaning if you use wire that is too thin you risk over heating the wire and causing a fire.
Edited: 10/31/2016: Removed mention of stranded wire
Please always use the appropriate solid core, correct gauge wire for residential electric for general safety and avoid fire
So if the circuit is 15 amps use 14 gauge
If the circuit is 20 or more amps use 12 or thicker gauge.
Chances are your light circuit is 15 amps.
But please use google and Home Depot to verify this .
If the old wires look okay, you can use the old black wire between the switches.
Note: Please confir with an electrician, theoretically solid core might be safer, less resistance, but I find solid harder to work with.
Note: every time I wired in a new switch I replaced the incandescent bulb with a new led.
The new led draws much less current than the old bulb, and thus less heat and less chance of fire.