Cavers do a lot of this, as do arborists, and they each have different styles and requirements. A lot of the gear is similar, but some is different. A lot of knowledge crosses over from rock climbing as well as canyoneering, but there are differences too, both in technique and equipment. You will hear the term "SRT" for "single rope technique".
Cavers use their own sort of specialized harness that is different from a climbing harness. It is all a question of whether you want equipment that is optimized for what you are doing. Caving harnesses tend to be more rugged and designed to endure abrasion. They also rig as low as possible to optimize ascending. The use a big D shaped specialized carabiner that is designed to be side loaded (unlike regular climbing carabiners.
One consideration is weight and bulk of gear. This is not so much of an issue if you are dropping from the surface. If you are carrying gear deep into a large mine to drop some holes, then it becomes a much more serious consideration.
I am still using my ATC and getting along fine. If I was going to "upgrade" a Petzl stop would be the likely choice. An ATC is light and simple. The stop would add safety and save your bacon in a handful of situations.
I also have a sqwurel device that some canyoneering friends turned me onto. It allows variable amounts of friction without the bulk and complexity of a cavers rack. Light and fairly simple frankly. Mine is a V2.
If you don't use a Stop or similar device, at least consider some kind of backup. I don't use one at this point in time, but many people won't even consider rappeling without one.
Tom's Old Mine Info / tom@mmto.org