I don't have a coatie GSD, but I do have a fluffy Keeshond (a double-coat breed) - and I trim her toe hair regularly. Not too short, just short enough to be flush with her pads. It definitely helps her to have better traction, and we have 90% wood floors with some rugs throughout our house. I used to trim it less regularly, but as she's gotten older, I'm much more on top of it than when she was a youngster.
As far as brush recommendations, you may get better/different ideas from GSD people, but I'd highly recommend a good undercoat rake, standard slicker, and a nice-quality pin brush. All part of our regular grooming routine!
Dover von Ziegeln Zage (GSD, 3 yrs)
Dutchess Lena of Black Lake RATI (Keeshond, 12 yrs)
“Once you have had a wonderful dog, a life without one, is a life diminished.”