Should I use Gorilla Glue or Crazy Glue for broken off handle of a ceramic mug?
The one with the biggest advertising budget.  

No seriously... 2-part epoxy.  

Toxicity -- the inside of your food cans are lined with it,  this is why tomato paste doesn't rust the can.  It can add trace amounts of BPA but only if you botch the mixing heavily toward the B-part.  

Dishwasher safety - make sure this epoxy is good up to 100C temperature.  It is impervious to water once cured.  

Speed - epoxies come in every imaginable speed from 1 minute to 24 hour cure. 

Durability - let's do the math,  epoxy + carbon fiber = Boeing Dreamliner. 

Surface fit - not super picky, as it is fairly thick... for better results modify it with a powdered adhesive filler like West System 404, which can gap narrow imperfections giving full strength. You're supposed to use West System fillers with West system epoxy, but I won't tell.  If you know a boatmaker, ask him for a teaspoon of the stuff.  Mix in til it's like maple syrup, not too much. 

I gather you would favor an epoxy on the fast side of the range.  Have a razor knife handy to scrape off any excess, during that sweetspot when it is solid but still rubbery.  It won't be like that for long.