I have seen variations of other board games or strategy games where the aim is to actually 'lose' the game by forcing your opponents to make moves. Applying this concept to the rules of chess, would it require a completely different set of skills and thinking to let your opponent checkmate you first? Is the variation of moves and the analysis of the moves different if the winning objective or condition is reversed?
Although selfmate is a popular type of chess problems, the concept you have described simply would not work in a chess game played from the starting position; your opponent would need to cooperate with you if you want to get yourself mated. This means that any game played by chess players of any skill level would almost certainly end in a draw under your rules, which unfortunately makes your question moot.
It would be a different kind of game. You'd still want to build up a material advantage to be able to force your opponent to checkmate you. But you would almost always need more material than that which is required to checkmate your opponent.
It would also be more difficult to win material by threatening your opponent's king since your opponent would only need to defend when a move to get out of check is required. Similarly you would need to worry about getting your king out of check but not about being checkmated.
More positions would likely be drawn than in standard chess so you could say the analysis is simpler in this sense. Then again finding a win when one exists would be more difficult for a random position than in standard chess so the analysis is more complex in this sense.
I write this as an answer (even if it doesn't contribute that much, but it would get too long).
If you ask any expert of the selfmate genre in problem chess, he will give you an immediate enthusiastic yes: Selfmate strategy is much more complex than n#. Here is an especially glaring example: Motive inversion. In "normal" chess, you will never make a move that hurts yourself, with only one exception: if you play for stalemate. In selfmate, you might play moves with positive and with negative aspects, even with both at the same time, and to top it, White might use the exactly same motive that Black used to parry a selfmate threat (say, unpinning a piece of his to harmlessly interpose a check), and use it for his own good (whoops, now the unpinned piece must mate). I googled a random example - try understanding the strategies of both sides without getting a knot in your brain!
That said, in a practical game, you probably don't need such fine details. Follow the advice of ericw31415 and user11382: win all the material of your opponent, except a safely blocked pawn. Then force your own mate by zugzwang. The minimum material needed is KQB/KP. If your opponent still has major force, say a Q, the "standard" strategy in long s# is "checking the opponent into place" until you can give the decisive check that immediately forces selfmate.