If I'm running a rim that has about a fingers width (skinny) of distance between the rim and caliper, is there a general rule as to the safe distance?

 

That's plenty Usually maybe an 1/8" is good enough. I've run some wheels really close before with no issues.

 

How about just a couple millimeters???

That's what my winter wheels look like on my 4 pots, but they haven't ever hit my calipers.

Here's what mine look like.

 

a finger width is quite a lot, and as long as you stick to paved roads, a few millimeters is even fine, if you play on the gravel the really tight clearances can lead to some scarring and cosmetic damage, but that's usually about all.

 

Then it kinda sucks that my few MM clearance is on my winter/rallyX rims only.

 

i used to rub

 

OP, you can always get yourself a 3mm spacer for extra insurance.