Beech is a wood that is used a lot for handrails and interior peices that need a close grain and will paint and stain nicely. It's a wood which has good workability. If you have enough of the beech to do the floor, just use that. The Walnut is really a special wood (especially Black Walnut) that should be reserved for something nice, i.e. table or gunrack, clock etc.
http://www.wood-worker.com/properties.htm#sectB Try that one. K10