What's the best 1/4" cable (brand, gauge, etc.) to connect a guitar amp head to a speaker cabinet? I have a run of under 10 feet. I read using an instrument cable can damage the amp and speakers.
The best bang for your buck will be to make it yourself: buy a good brand of plugs (neutrik, switchcraft, etc) from Markertek or equivalent and use plain old 2-conductor AC extension cord for the cabling. Banana plugs or Speakon are preferable to 1/4" but not terribly common in guitar rigs.
Make the cable as short as possible, but not too short!
While you should use a cable designed for the job, this is not because using an instrument cable will damage speakers or the amp, but because an instrument cable is designed for low noise and low current, a speaker cable may have significant current going through it so needs to be able to cope with high power.
(Actually, I guess if the cable does melt, a short circuit could damage the amp, so yes - it could damage your amp)
In terms of brand or gauge - it really will not be important which you choose. There is an awful lot of hype over cables which may have x% oxygen, or gold foils etc, but this application is not generally one which requires a top spec signal to noise ratio, so a screen or shield is not needed (unlike your guitar lead which will have a shield to try and prevent mains interference etc)
It would also be an unsuitable question here as the 'best' brand may change over time or from location to location.
Just look for cables described as 'speaker cables' - ideally ones with "Speakon" connectors if your speaker cabinet has that type of connector.