14/4 cable use in switches for vent fan and light combination
Any 14/4 you can find should do it.  Ideally you want NM type, but UF will suffice. 

I expect any 14/4 on the market will be solid wire. 

If a conduit connection is feasible, you can then run individual THHN wires in conduit. This may make sense if thecost of 14/4 is prohibitive. THHN wires come in solid or stranded. I prefer stranded, but I am pretty good at getting stranded wire on screw terminals without frizzies.  You must never use stranded wire in a backstab.