I don't think it matters much, since you don't have to visit every level to beat the dungeon. It's possible to beat the dungeon without ever visiting Lower or Terraports. From lowest elevation to highest, the order is
- Lower
- Entrance Level
- Underpaw and Ancestral
- Upper North
- Upper South
- Terraports
If you're hoping for a more natural order, here are the connections between floors. Players start at Entrance Level (obviously).
- Entrance <-> Lower
- Entrance <-> Upper North
- Upper North <-> Upper South
- Upper South <-> Underpaw and Ancestral
- Upper South <-> Terraports