<< vinyl tile looks like it's the cheapest 86cents a square. >>
Don't even think about using something that cheap in your kitchen. It has no
top wear layer like the quality tile and will look like crap in a year or so
around the sink and stove. The bargain tile will also shrink slightly over time
and leave some ugly gaps to bug you. Armstrong and others make tile with a
polyurethane top coats that will give years of good service.
<< Or can I lay that directly on the floor (wood)? >>
Can be done if the floor is not bare (unfinished) wood and is smooth. Pros will
level floors with specialty compounds or autobody type fillers and sand and
then topcoat with sealers, varnishes or paints to present a good substrate for
the tile. Some like underlayments if the floor looks beyond upgrading but all
the nailing needed to keep it from feeling spongy underfoot can be a negative.
Added height may also affect doors or molding with underlayments. Choose wisely
and good luck.