You didn't mention what type of foundation you curently have or what's on your floor right now?
If a contractor said he could do tile for just a little bit more than linoleum, than he's lying to you, or you have picked out the very highest grade linoleum there is.
Lets pretend your kithchen is 100 square feet for the sake of argument. One sheet of lenoleum will cover this easily and cost you about $100. This is an easy one day job, so glue and labor should run another $200 to $400 depending on your area and your installer.
Cheap tile starts out at a buck a ft, but it's pretty bad in most cases. Nicer tile is gonna be $3 a ft. If you have a wood subfloor, you will need to put cocrete backer board down. Never install floor tile directly to wood. It will buckle in time and either crack or pop out. Backer board is gonna cost you around $80. Thinset and mortor will run another $40. This is a two day job if all goes well, but could be three or even four if the subfloor isn't level or needs some work. I'd guess labor at $400 to $1,000.
Cost for tile will easily be twice as much as linoleum and that's being very conservative. It will probably be three times as much by the time you're done.
Another option is floating a laminate flooring. Patterns and styles vary, but it's not a tough project and allot of do-it-yourselfers put them in all the time. I know a few ladies that have done rooms by themselves. Cost for the laminate will be between linoleum and tile.
Tile will give you the best resale value. It's cold to bare feet and very easy to clean. Light colored grout will stain, so use a darker neutral color.
Linoleum is the cheapest and easiest to install. It has the lowest resale value, but if it's clean and in good shape, won't affect the sale of an entry or midlevel home. Linoleum does tear and is damaged fairly easiliy. Sometimes it's easy to repair, other times there's just no way to fix it. Just moving a fridge can tear ro put waves in it.
Laminate gives you allot of bang for you money, but it needs to be kept dry. Most people don't have wet floors, and they are fine with getting wet for short periods of time, but will buckly and fall apart if flooded.
I have no experience with cork flooring.
From what you posted, I'd find another contractor and get a few more opinions. I think he gave you bad advice to get the job and I don't trust him to do anything else.
Good luck,
Eddie