Birch is you best bet. It's all according to what you are gonna do with it, birch is good with it all. If you are staining it you really need oak and the two coats of polyurethane, it you will paint it, pine is the cheapest and east an sold to work with. Hope I've been a help, been there, done that!
I would choose Birch or maple since both woods are very smooth and not subject to splintering (as in getting a splinter by sliding your hand along the rail). Both woods are easily worked with hand tools and provide beautiful finished products.