I've gathered the requirements for the different dungeons (pet / item requirements) listed them, and sorted them by "most important" to "least important" requirement to meet (useful when you have limited pets / item slots, or looking for what class to evolve next).
Pet and Item Requirements
This image displays the pet criteria and item criteria to meet events in each dungeon.
You'll notice I marked health potions in red - this is where I felt the cost of bringing the item along didn't justify the reward - especially if your pets are taking damage and consuming health potions outside of the event.
The ordering is my own, but is primarily based on the *probability* of encountering an event that has that criteria. Those probabilities were then slightly weighted based on how "desirable" it was to succeed at the that event, or how "severe" the penalty for failing the trap. The weights I used are below, as well as a brief description of what's good/bad about each event.
All Events and Traps
Here is a tabular list of all events and traps that I used to come up with my pet criteria summary and priority order.
Note of that depending on the dungeon depth you're running, D1 / D2 events change probability. I've got some additional columns showing the adjusted probability following my priority weighting scheme.