Oak.

mahogany

Painting these or staining?

Oak. Like your floors. If you're going to paint, maple is a very expensive wood for painting. There are other, less expensive paint-grade closed grain woods.

What is the style of the house?

What does that mean?. Is the house a Victorian? Georgian colonial? Saltbox? Craftsman?

It depends on several things. The finish of the floor and what kind of oak first. Will it be dark or cerused? American red and white oak are open grain woods. For flat cut(most common) the open grain turns black when you stain it. That gives the wood a two dimensional look. Cerusing fills the grain with a lighter color(usually) and can blend things if you want a lighter finish. Second the width of the planks. And whether the wood surface will be distressed for a rustic effect. Post a pic of the flooring for more specific feedback. If you choose oak for the cabinetry you can avoid the black grain 2D effect by having everything made with quartersawn and/or rift cut red or white oak. You can look up Images to see the dif as apposed to flat cut. Amish woodworkers can be a good source.

Cherry is a beautiful cabinet wood, but it depends on the look you want.
You also can customize cabinetry with stain color, distressing, etc. I'd create
an ideabook of libraries you like and see what the details are to
replicate the look.

Here are some ideas:

Stained dark

Urban Cottage · More Info

Painted dark

Hurndale · More Info

Painted light

Beach Style Family Room · More Info

Painted cherry...? OMG! Surely not...

If you're going to paint them, poplar is probably a better choice.

Diana Bier's photos are a lovely set of options.

I'd add that it depends on how formal or casual/rustic you want it to be. Oak or knotty alder tends to be a more rustic look. Finer grained woods like clear cherry or walnut often more formal. The style and design of the millwork will also change the feel.

I always felt if there was wood grain showing in a library it should be . . . bookmatched.

HAHAHA! Mark strikes again!