You don't need to stick to one type of flooring - it could be an interesting effect to use different sorts in different areas.
Anything that is easily cleaned and won't discolour with bleach splashes and so on is essential. Something warm to the bare feet too.
I think a very good quality vinyl cushion flooring is ideal and need not look 'cheap and nasty'. It pays to have a professional fitter lay it on top of good quality underlay, if necessary.
If you like you could use those lovely rugs that can be machined washed on top of the vinyl to add a bit of variety and colour.
Tiling is smart and hygenic, but cold unless you have underfloor heating. Tricky to lay in awkward places too.