The pedals that you choose to buy will come with matching cleats. Shimano SPD cleats will not work with crank brothers pedals, but it's no problem because they are included as a package, with no need to buy them separately. I don't see any pictures of the bottom of the shoes, but assuming they are like every other "Mountain biking" shoe out there, they will have the two-bolt mount on the bottom, and will work with any mountain pedal/cleat pair that you decide to buy.
Clipless is the way to go. Time to learn how to pedal circles.