Ok, according to this site:
Red Oak finishes and stains easily. It has none of the blotching problems that are associated with birch or maple. The open pores absorb more stain, so the grain pattern becomes quite evident when a dark stain is applied to red oak. If you hope to achieve a near glass like appearance with the top coat, it is almost always necessary to use a pore filler. For effect, try top coating a couple of times and then tint the pore filler a contrasting colour, fill the pores, sand and then top coat again. The effect is quite fascinating.
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So it appears that you’ll be able to use a dark stain with decent results on this wood. Here is the guide to Minwax stain colors. Depending if you want it more to the brown side or more to the black side, maybe ebony, onyx, jacobean, classic black. A little lighter, but definitely brown, walnut.