In the first place it is easy to rank the materials according to price. Basically, stone, whether it's sandstone, slate or some form of marble will be very costly. Wood varies enormously - wide, reclaimed French farmhouse boards are very dear and thin slivers of oak on a plywood base aren't if one is prepared to shop around a bit. Ceramic tiles are comparable with the lesser end of the wood world depending on size of tile. By far the cheapest option is vinyl floor tiles, although there too there is a wide range in terms of cost and corresponding quality.
When one thinks of maintaining floor surfaces one is thinking of basically two things; sealing and cleaning. Natural materials like stone and wood need regular application of a protective layer to prevent the underlying material becoming stained in the hustle and bustle of kitchen life. Ceramic and vinyl floor tiles do not (Although porcelain tiles do need a one-off treatment)
Failure to keep up with the maintenance of stone will lead to unsightly discolouration and with wood, inconvenient and immensely disruptive floor sanding.
Cleaning wood and stone in a kitchen environment takes more effort than the ceramic and vinyl alternatives simply because of the grain of wood and texture of stone which creates little hollows in which grime will accumulate and therefore require hard work to remove. Ceramic tiles and vinyl flooring are usually completely smooth in texture and can be cleaned as easily as in television commercials.
With ease of installation vinyl flooring is the easiest, a craft knife is about all you need. Wood, if one is confident with a saw, is comparatively straightforward although there is a difference in complexity between 'click-click' laminate and complete replacement of boards. Ceramic tiles and stone require water, specialist cutting equipment, cement, grout, goggles, a truss for when you've wrecked your back and probably reinforced joists to take the absurd weight of a two inch thick layer of the Jurassic era in your modest terraced house.
So what's it to be?