Drop shot line

If you're fishing 10' deep or more with the drop shot, I wouldn't go any lighter than a quarter ounce with the weight.   I generally use that or a 3/8 oz with my finesse set up if there is much wind.   My reasoning is that the drop shot system is a way to present the bait a little ways off the bottom, so I might as well get the bait to the location ASAP.  Your bait is essentially weightless, no matter how much weight is beneath it.

My current finesse drop shot rig is a 7'St. Croix Mojo spinning rod - Med action with an extra fast tip and a 2000 size Shimano spinning reel.  Line is 14 lb Fireline Crystal to a very small ball bearing swivel, then connected to 5' or so of 8 or 10 lb Abrazx fluorocarbon.  All casting with this rig is an underhanded pitch as the line won't reel past the swivel.   Not really a problem as I rarely pitch more than 40'.  Like several others here, I like the strike indicator characteristics of line contrast against the water.