I'd pick whichever white leans a bit "warmer" rather than cooler, given your stained wood cabinets. As for cabinet hardware, I like to match the finishes of the plumbing fixtures with the handles/knobs. So if, for example, your faucet is a polished nickel, find cabinet hardware that is also polished nickel. Same for light fixtures, too.

White Dove is my preference.

You have to look at it with the lighting.

I have Simply White and love, love, love it in 99% of my house, but one room has very different lighting and it reads a little yellow in that room. It is perfect in all the other rooms.

Agree...White Dove.

All three of them are amazing colors.

White Dove is what many of the standard box stores use for white. Simply White was color of the year, because of the properties it has. Chantilly Lace is cooler and brighter than the other two, which would appeal to some people and which would be too sterile to other people.

I would help to have some photos of your woods, but typically the Hickory is varied tones but all to the orange yellow side. I would do a "pure" white. I would want to know how much natural light you have and what your flooring will be. As to hardware, that depends on the style you are going for. I assume that since you picked Hickory, it will be more mountain/lodge? If that is the case, you don't have to match to faucet hardware finish in fact, black matte would work well.

Modern with rustic woods, using stainless long pulls.

More traditional look with black.

This kitchen used rubbed oil bronze. So you can pretty much choose what you think work with the "style" you have going. Go pick up several different examples of roughly style and finish you want and test them out with your cabinetry. Lowe's actually has a great selection and at reasonable pricing.

Thank you so much everyone!!!

Our kitchen is on the SE corner of the house with lots of natural. Which or the two, simply white or white dove, would make a better fit? We are planning light oak floors and marble counters.

I should have noted, I'm looking for cabinet and trim color.