So....finesse fishing is something I enjoy doing just as much as throwing bigger baits, and I've been doing it since the 80's. My setup is as follows:
4 rods (all are 1/16th or 1/8th oz):
Dropshot rig
Splitshot/slipshot rig
Tube
Small football jigs/finesse jigs
On the first two, I can rig a wide variety of finesse baits - 3" grubs, 4" straight worms like the Roboworm, reapers, 3" Senkos, 3" minnows, Zipper Worms, Flat Worms, Super Doos, etc
The tube rod is always rigged with a 1/8th oz weedless 60-degee jighead. Sometimes I'll use a 90-degree jighead if I want more spiral-falling action
The last rod, I use for hula grubs, 3" grubs, and small craws on the football jig. I'll also tie on ned rigs, hover rigs, hair jigs, darter jigs, and finesse jigs.