In 3 check, I believe white has a forced win from move 1, due to the highly dynamic nature of the game - white can play 1.e4, and black is almost forced to go for ...e6 later, allowing white a lasting space and activity advantage later (if played properly).
Also, one check is not a big deal in 3-check. You want checks in combination, and if you sacrifice a piece for a single check, and no more (compensation, extra checks), it's usually a bad move.
I don't know that much about 3-check, but basically you need to play very solid, yet expansive chess. Development of your pieces is especially important.
I just played in a 3-check live tournament. I wonder what are best openings. 1. Nc3 and 1. e3 seem to be the most popular moves. 1. Nc3 allows to sacrifice your knight and to make the first check in a virtually forced manner (Nc3 -> Nb5 -> Nc7+ / Nd6+ or Nc3 -> Ne4 -> Nd6+ / Nf6+).
Any feedback is welcome.