How tight should the front deraileur cable be when on the smallest chain ring? Should it ever be slack?

I don't like slack but it depends a little on the shifter.

For example, if you're using a non-indexed Grip Shift and you're anal about having the "2" indicator lineing up in the middle ring you may have to tolerate a bit of slack in the cable when you're in the granny.

Yes it's normally slack. You use the inner limit screw to determine the position for the smallest chainring, and the cable should be slack enough to allow it the FD to rest against the limit.

On a triple, the cable tension is set based on middle ring, while ensuring that it also shifts effectively to the larger. On a double the tension is set based on smooth shifting to the outer ring.

The systems are designed with slightly excess travel for each click, so the cable be slack on the inner, and slightly stretched while on the outer, where the outer limit is used to fine tune the position against what would be a slight overshift.

I've got Shimano 200GS deraileurs with 3 chainrings. So just to make sure I got this right it should be taught (not slacked but not overly tensioned) on the middle chainring. And I can expect to have a little slack/droop in the cable when shifted to the smallest chainring.

And if it is a road bike then it has to have slack and each deraileur and shifter has a litte different tension requirement. So the way I set all of my bikes is when in the smallest rear cog and the middle ring for triple that the chain just clears the outer portion of the deraileur cage plate.If the chain rubs in that combo unscrew the barrel adjuster out until it stops rubbing. This will give enough tension to shift to the big ring as well and then adjust out any extra play in the front deraileur.

While we thing in terms of tension, it's actually position that determines the correct adjustment. The cable transmits the position set by the clicks in the lever to locate the derailleurs correctly with respect to the sprockets. So don't think of how tight the cable, but how long. You adjust is so the FD is in the correct position, and shifts smoothly to the middle chainring from either direction.

The other two sprockets flow from there based on the spacing of the clicks in the lever, and are fine tuned by the limits.

No. It should be taut when in the smallest ring because the cable is relaxed. It should, and will, be tight in the middle and outer rings because you are putting a lot of tension in the cable to move the derailer. The tightness of the cable should be about the same whether it is in the outer or middle gear.

If the cable is too loose in the small ring, the shifter may not be able move the cable enough to effect a shift.