What is the minimum item level recommended for putting it on an auction house?
If you are talking about random BoEs you find while leveling, then ilvl doesn’t really matter. It’s about how desirable the piece is for transmog. If you are talking specifically about level 60 BoEs, it can be a bit more complicated.
The best advice I can give you is to use an addon like The Undermine Journal or Trade Skill Master that can give you an idea of how much people are listing stuff for on the AH. Just keep in mind that BoEs can move slowly, so if it’s got a big deposit and only a modest list price, it may still be worth vendoring/DEing rather than relisting it a bunch of times.