The important thing is to choose a branch where no monsters will spawn, that would pickup or destroy the stuff you drop. Monsters do spawn - even if you cleaned a level or branch - but on Lair and Hive there will be only animals. They do not pickup stuff.
The suggestion to build your stash on the second level of such a branch comes from the fact, that monsters can take stairs. You wouldn't want to welcome e.g. red jellies or acid blobs with open arms while standing at your stash
And the decision to build a stash in Lair or Hive depends only on the depth of their entrance in the dungeon. If you're cleaning up branches of the Lair - build it in Lair. If the entrance to the Hive is deeper in the dungeon and you are cleaning up the Vaults and its branches, choose Hive. But the 2-3 levels in difference usually don't safe so much travel time.