What levels should theoretical endings be learned at? When I am introducing beginners to the game, I immediately teach them KQvK, KRvK and KPvK. I follow that up with KBBvK at around the 800 level. Are any resources on when one should learn/teach the following techniques: Lucena win, Philidor draw, KBNvK, KQvKR, KRBvKR, KNNvKP? Each of these teaches valuable lessons with applications beyond just the endgame but the last two may not be worth studying seriously until the IM+ level.
The more I look at Silman's Complete Endgame Course, the more I agree with how he has organised it. 


Overkill mates where the stronger side is up by at least two rooks worth of material. KQQk, KQRk and KRRk. Especially KRRk is good because it emphasises the importance of having a plan. With queen(s) on the board, mindlessly checking might let the student accidentally fall into a mate, but checking over and over again in KRRk is unlikely to produce progress. 
KQk and KRk. The two basic mates. Further hammering in the importance of having a plan. 
KQkb and KQkn.  Easy enough to win, but especially the latter one takes surprisingly many moves against a stubborn defender. 
KPk, opposition and the square of a passed pawn. Nothing much needs to be said. This is obviously required knowledge.  


These four represent what I'd call the bare minimum needed. And the third is really more of a case of "head fake learning". When one is better at chess, one can obviously figure out how to win KQk{b|n} over the board, so from the viewpoint of teaching theory this is at best marginally useful. The student is actually learning about what the pieces can and cannot do which is always going to be useful.

Beyond this, I think the most practically useful are KQkp, Lucena, Philidor (the KRPkr draw, not the KRBkr win) and a small selection of minor piece theoretical draws (wrong-coloured bishop + rook pawn, KNPk with pawn on h7, etc.).  

You want to minimise memorisation while maximising useful knowledge gained for practical play. Not just in the endgame but also the ability to formulate and execute plans (try KRRkr for this) and gaining familiarity with the capabilities of the pieces.