It sounds strange, but most of the time I set the white balance to daylight. No matter what lighting conditions I shoot in. I do the white balance in lightroom afterwards, that saves me some time when shooting, especially if there are different light sources, or the light source changes a lot during a shooting.
If you balance on a greycard, or all three grey, white and black, and use that to set your white balance in post production, the software will use this point as neutral. In general I like it warmer though and adjust the sliders accordingly after that.
When shooting with flash, daylight white balance setting usually works pretty well (at least with the flashlights I use), but again you can change that later as long as you shoot raw. And yes, I´d rather balance the flash than the available surrounding light.
When shooting with flash, consider setting the exposure for the rest of the room and only use the flash to fill, whenever possible. It will add some grain, if you pump up the ISO, but the image will be much more lively. If you don´t flashlight will light the foreground much more than the background and so the background will be way underexposed, while the people will all be bright - that´s a rather unnatural look. I hope you understand what I mean.