It depends on just what effect you are trying to achieve.
Obeche is a very bland wood, which isn't altogether a bad thing. But if you are staining to try to enhance the
grain pattern the the result is likely to be disappointing because the grain pattern is rather uninteresting.
Staining works great on denser woods that have an attractive grain - Oak, Ash, Walnut, etc.
I'm doing some black frames in Obeche at the moment. My usual method is to fill the pores in the wood with fine surface filler,
scrubbed into the pores with an old brush and slightly diluted. Akin to soaping your face prior to shaving.
I go over it with a J-cloth to remove the excess and level off the surface. When dry all it needs is a quick sanding.
Next two coats of acrylic gesso. This is sanded when dry. I finish off with two coats of black "artist's" acrylic which has a coat
of wax applied with fine steel wool and buffed when dry. This gives a nice deep 'ebonised' look with a nice sheen.
There are many variations. e.g. using a undercoat of Red Oxide and rubbing back the high points in the waxing stage to reveal
the red underlayer. Dusting with Rottenstone before buffing and while the wax has not quite dried can look good.