Finesse is a style. Like in tennis, you have finesse players and power players. Same equipment for the most part, just different styles of play. Finesse players will stroke the ball differently, often play full court whereas power players tend to stay at the base line and power the ball over the net. Stefan Edberg, John McEnroe were finesse, someone like Andre Agassi was power. Although both did all styles, these were their primary styles (IMHO).
That said, when I finesse fish, I tend toward lighter gear, softer presentation. I won't normally use my MH baitcasting setup for finessing, though I can.
I finesse fish 99% of the time with both spinning and baitcasting gear.
For baits, Senkos (sometimes knockoffs, but Yammies work best for me), Zoom Finesse worms, and sometimes when the bite is really tough I'll throw wacky rigged Zoom tiny flukes in watermelon red flake. That'll net me a lot of smaller fish, but I've caught some beasties, too. I'll rig Wacky, weighted wacky, Texas weightless and Texas weighted.
If I'm throwing lures I'll tend toward lighter lures, not fist-sized cranks or such. But again, you can finesse those.
Hooks: Gamakatsu Finesse Wide Gap #4, #2, #1. I caught my PB 7.5 lber on a size 1 or 2 in thick weeds. These pups don't bend or break. Caught 5+ lbers on the #4 size. These hooks rock.
For gear: Primarily Shimano Stradics 1000FI, 10lb braid mainline, leaders mono, copoly, fluoro from 6-15 lb test. Shimano Compre rods, Medium power, X-fast action, shorter (5'9", and 6'3").
Line brand: I use Power Pro yellow, and mostly P-Line Floroclear mist green leaders. Brand is really up to you and what you like. Opinions are all over the place, but the bottom line is use what you like and feel comfortable with.