By all means try Teak oil on it and see if you can live with that.
If not and staining is the next option I'd recommend a stain made by ML Campbell ML Campbell Home
if you can find a distributor near you. Minwax is a dumbed down stain for the masses and I find that it often does an unsatisfactory job. The ML Campbell stains are oil based and are much more likely to give you a uniform looking finish once done. Their stain can be applied with a rag. I'll bet that they make a pigment that is close to teak.