Mr. Doug,
It's either very important, or makes no difference at all.
If the characteristic impedance of that coax is the same as the rest of the system, or at least close, it makes very little difference as far as the characteristic impedance goes. So, select a coax of the right impedance.
Power handling ability. It actually amounts to voltage handling ability, how much before the stuff arcs over, or get's too hot? High SWR, or impedance mismatches can raise the voltage to really, really high levels. Only part of that applies to the actual power put into the stuff. More is better to an extent determined only by you.
Losses. All coax has losses. Those losses are determined by frequency of use and length, for any particular size/type of coax. Until those losses get to something like 3 dB, you will never know it or hear it without using 'lab' grade testing equipment. If you are talking about 1 dB of loss, or a fraction of a dB, forget it. RG-58 coax has a bad reputation, but it's only because it was used beyond it's capabilities. The same can be said for ANY coax if it's used beyond it's capabilities. Knowing what those capabilities are certainly helps. At HF, most of the 'high end' coax is vastly over rated. Doesn't hurt to use it, but it's certainly not nece$$ary for the average person. Suit yourself.
None of this tells you exactly what to use, does it? Nope, you need to evaluate that for your $elf.
- 'Doc