From what I've heard it is one or the other, stain or oil. Stain will not take if there is oil in the wood and oil will not be absorbed if the teak is stained. Oil is supposed to be better for the wood, as teak has its own natural oils. Also, I think that teak staining is recommended for applications that will not be IN the water, like a swim platform is. It is more for sailboat decks.
With that said, I used a three step system from West Marine last year and the wood was white and fuzzy after just a couple weeks. This year I used the Starbrite 3 step system, but after the cleaner and brightener, I sanded the whole platform with a random orbital sander and 120 grit paper. After thoroughly rinsing it and letting it dry for a couple days I oiled it. This was all about 3 weeks ago and the teak still looks brand new. Definitely worth the effort.