Traditionally, vinyl and linoleum have worked well in this active space, because they can handle moisture, have safe nonslip surfaces and are easily maintained. Vinyl's resiliency is an advantage. Ceramic tile is somewhat resilient, but grout problems and chipping are common areas of concern.
Consider the durability of the floor covering. If you have small children, the floor needs to stand up to scrapes, dents and spills. Both hardwood and vinyl work well in these situations. Wood, though, will take more maintenance. Additionally, vinyl and linoleum are softer surfaces than tile -- an advantage if you spend several hours a day in the kitchen.
Take into account your budget when making the choice. If upfront costs seem low, consider the long-term maintenance a particular floor will require. Wood requires staining or refinishing over the years, whereas vinyl or linoleum require little other than cleaning.