How do I choose which adhesive or material to repair action figures?
It depends what you want out of the repairs.

If you're looking for longevity and quality of repair, an epoxy (resin) is your best bet. They tend to create the best seams and are difficult to break. The downside of these is that you get one shot - getting it wrong quite often either gets the parts stuck in the wrong place, or you very messy. Some epoxy glues also require mixing of two ingredients, which is definitely messy.

For quick-and-dirty repairs, it can be better to use superglue (acrylate-based glues). This takes longer to set, in general, and won't last as long, but can be useful for repairs that won't see much stress or that don't matter too much. Be aware that you can't use superglue on all materials - notably, acrylic won't take well to it.



Information from my own knowledge, supplemented by the information available here.