If you have a DAC which upconverts, it's a safe bet that it'd do a better job than your soundcard in your computer, so in that case, set Foobar to 16 and let the DAC upconvert if you want.
Since my knowledge on 24bit is limited to say the least, I did a quick search with Google and found this recently updated FAQ (took about two seconds). Also found this forum thread containing this post:
If the setting is at 24 bit and your file is 16-bit, the lowest 8 bits will be filled with zeros. No loss, no gain.
If the setting is at 16 bit and your file is 24-bit, the lowest 8 bits will be either truncated, or truncated after dithering, and you will loose some information, though the difference almost surely won't be audible.
So if you care about that, leave the setting at 24-bit.
But if switching the setting for each file really makes you happy, then you may do that as well. I personally prefer to focus on the music not on switching settings.
I recommend enabling "dithering" if you're using 16bit. It will somewhat limit the quality loss of downconversion from 24 to 16.
Hopefully that answers some questions