Tile or engineered wood floor(bamboo)

Tile will be cheapest as linoleum might peel up.

Labor is always more costly than materials. But, the best *material* would be tile. It's also one of the least expensive, and easiest to learn to DIY.

Hardwood. Any material has its pros and cons.

"Best" and inexpensive rarely go hand in hand. Most bang for your buck = ceramic tile...but install can be expensive. Ceramic, porcelain, concrete, sheet lino/vinyl will offer water proof floor (cork glue down as well but you need to run it under the cabs to get this benefit). Everything else will offer moisture "resistance" but you still have to move quickly to clean up spills. Bamboo is a no-no in a kitchen...I've seen the heart ache...it isn't pretty.

Sheet vinyl/lino still are "top of the heap" when it comes to performance + cost + choice + install. You can always find "ends" or sales on these products. They require professional installers but if you have a small enough kitchen it can be pretty easy on the budget.

If you really want cheap = peel and stick vinyl. Goes down over plywood or concete. Lasts until you decide to rip it up. It all depends on your "splash style" in front of the sink...if you do not wash very many dishes by hand and very little water hits the floor (a few times per week) almost any floor can handle it (laminate may not).

If you are energetic with your hand washing of your dishes and you are splashing/spraying the area several times per day = ceramic/porcelain/cement. If you are somewhere in between then the lino/vinyl sheet products or peel and stick will do the job as well.

In essence it comes down to your comfort level. If anxiety hits with the thought of water damage then work with ceramic/porcelain. If you take a more nonchalant approach to water and flooring then just about anything will work. Know your limits and know your flooring's limits and you will be fine.