Since this is regarding a Hollow World type setting, I'll ignore factors that would alter the cave ecosystem from a modern standpoint, as in contaminates.
Do you find colors intense or more subtle?
It depends. High water, such as floods, can cause formations to be dirty, leaving a dull look towards them. While caves with a lack of rising water, or multiple levels, can have a pristine and bright color.
would the colors tend toward the darker or lighter?
Both. As stated above, it would depend on the cave itself.
Do you find various colors close together, or more monochromatic sections?
Together. Remember, formations are formed by the flow of water through the earth. The coloring of formations is determined by what is mixed in with this water flow. For instance (sorry, modern standpoint), if there is a sinkhole located on the surface that is full of junk, such as rusting equipment, then those contaminates are going to eventually find their way into the cave system and become part of a speleothem, thereby altering the coloring.
Would a single stalagmite have multiple colors - like bands or stripes?
Yes, it could. I've seen formations that were primarily a beautiful white, only to have one section with a downward stripe of an iron color. Just remember, stripes will typically be vertical, with slight horizontal deviations based on air flow.
Thanks in advance for any help you brave explorers of the netherworld may be able to provide.
I'm not sure how the above will help, but I hope it does.