They vary in size and can be connected to eachother for really long pitches. SRT - Single Rope Technique. This is somewhat of a beautiful skill that has been developed and perfected in fairly recent years. Rope - although climbing ropes can be used static ropes are the best. Preferably between 10.5 and 12 mm diameter.
Length depends on the cave.
Descender - this is a gadget to will allow you to get down the rope. Ascender - this allows you to get up the rope again and you need two. Various carabiners, maillons, spanners and bolts. I won't go into details. The whole universe of techniques and the tricks would be too much to go into here but just buy the kit and find somebody who knows what they are doing, become their friend and go SRT'ing.