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my apartment has NO usable chefs knives. No set, nothing big, everything is dull. I'm willing to spring a little. What should I get? (kit should include sharpener)
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Get one big chef's knife. It doesn't have to cost much, just be comfortable in your hand.
I have a set of Wusthof knives that were moderately expensive, but I still like using the Chicago Cutlery chef's knife that I paid $20 for about 15 years ago. It's a little lighter than the Wusthofs, but is sharp as hell and very comfortable to use.
http://www.amazon.com/s/ref=br_fq__all/1...availability=-1
As for the rest, try sharpening what you have - I bought this sharpener for $12 at Ace hardware and it does a great job: