The wipe-down thing you're talking about is only an issue with steels which stain easily. You won't have any problem finding a good, stainless Japanese knife in your price range.
The big advantages you get with a good Japanese, European style chefs knife are: (1) Their edge taking and holding properties -- both singly and in combination -- are so much better than just about anything else. (2) They're light and, in combination with their sharpness, tend to be less fatiguing. (3) They're thin and can take a more acute angle, are generally easier to profile (set the angle), and don't wedge. And (4) Can be profitably steeled, just like a good European knife.
My feeling is that these differences are apparent against just about mainstream knives at a similar price made just about anywhere else. But compared to an essentially disposable $10 knife, the differences are so vast in edge holding alone, that it's barely worth making a comparison. It's my feeling that the law of diminishing returns doesn't begin to kick in until considerably north of the type of knife Ice recommended. You could, I suppose, make a colorable argument that something like a Forschner Fibrox -- at around $35 -- might be the best knife for the environment.
You should at least be able to get through a shift with a Japanese knife without feeling the need to hit the stones. I don't think I could do that with many stainless knives made elsewhere.
Of course that, as well as the question of whether or not a Forschner or other Euro is going to make the short list of your consideration, depends on what your standards for sharpness are, and your ability to sharpen.
Staying off the stones is one thing; you'll still need to steel on an appropriate steel. And if you're going Japanese, you'll need at least a couple of decent water stones, or a combi-stone. That means budgeting.
At the end of the day I'll probably end up recommending a MAC Pro (because I usually do) and a couple of other knives. It depends on your taste in knives, what sharpening equipment you have and know how to use, and your ability to stretch your budget.
Do you know if you prefer a French or a German profile?