From my highly limited experience and *assuming* from the wording of your question you'll be heavily leaning to rock climbing methods and equipment..
Don't think of this like climbing anchor building, you won't be linking nuts, friends, etc for anchors like climbing. The majority of vertical caves, especially! the popular srt ones will have bolts for anchors, so don't turn up with trad climbing gear.
Also make sure your ropes are semi static not dynamic climbing ropes. A bunch of screwgate locking krabs are good (try to avoid twist lock style ones as they don't self close when dirt gets into them). Also, you can use GriGri as a descender but they can twist the rope on descent a bit, not a problem when ab'ing off a crag but when there's a rebelay below you there might be a bunch of twisty tangle. I rigged on descent once (with a stop as my descender) and a mate followed me using a GriGri and found it a pain as he had a load of twists to negotiate at rebelays. Also GriGri is very drop-able so I don't recommend them