Beginners often spend too much time memorizing opening moves without an understanding of opening fundamentals. The beginner will become easily confused when his or her opponent varies from memorized lines. Therefore, beginners are well advised to initially avoid memorizing opening moves. "Openings teach you openings. Endgames teach you chess!" (Gerzadowicz)
Endgame theory is well established. Whereas, opening theory changes with each new innovation. Therefore, you can be confident that time spent learning endgame theory will not be wasted. Besides, it is easier for the beginner to comprehend the movements of few pieces then of 32 pieces.
One thing is clear, a student of the endgame will usually reach a happy ending!
I think it would be good to study king and pawn endings. I find that there are a number of games where I need to decide whether to trade in to a king and pawn endgame.
Rook and pawn endings are also important. When I played in tournaments regularly, I understood these endings well, and so I often went into a Rook and Pawn ending down a pawn, and still won the game.
Bishop vs. Knight endings might be next. The Bishop is usually better, if you know how to play this type of ending.
I would start studying these shortly after you know enough opening strategy to sty out of trouble for the first 5 or 6 moves, and enough about the middlegame so that it is rare that you give away a free pawn or piece.