While you might get a few people here to weigh on on a color decision you'll probably get a lot more input in a design category. Your's is more of a design question where this is more of a technical forum.

Personally I feel that natural color on Red Oak goes well with almost everything. Using oil poly will bring out the color of the wood but will yellow with age. With water based finish you can use a sealer that approximates the same look or you can use a very neutral colored sealer like BonaSeal and coat either one with a clear, non-ambering finish. This could be very close to the color of the birch and counter tops but floors will generally have more variation than those, so it will coordinate with similar colors without looking too matchy.

If you want to stain it darker there are about a million things to pick from.

Everything JFCwood said i stand by. red oak you're going to get some pinks, if its not too late maybe look into a different species? the pinks in red oak will be less prevalent with a water borne sealer like Bonaseal.