New knives for culinary school
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Wow! I was going to recommend you a Tojiro DP 240mm and it used to be $52 now it's $76 ! Still best performer for the money IMO. Not too flashy, just don't talk it up to other students or it will get stolen.
Nothing wrong with 10" chefs. I use a full size cleaver so anything less than 270mm gyuto seems short.
Whatever you do, learn to sharpen.
As for price, I'd like to keep it under $100 if I can. But I also realize it's better to spend a little more up front, especially for something I'd use everyday, than buy a cheaper one that needs replacing every few years.
Might be worth investigating what stones yall have as the best long term solution to keeping a high level of performance regardless of whatever knives you have. This is one of the biggest things that affects lifetime of knives (usage patterns, maintenance and sharpening)
Another <100 option is the Fujiwara FKM
http://japanesechefsknife.com/FKMSeries.html#FKM I would imagine these run a little thinner than Tojiro DP but not totally certain on that. Regrettably the Kanetsugu Pro M which I have gotten before as a gift has gone up in price, but it's thin grind, well finished knife.
"Professional" sharpeners vary widely in quality with the vast majority being a guy with a belt sander. Taking too much metal off, not thinning the knife, heating the edge, ignoring geometry. Buy stones and you can get ANY knife you want. Use sharpening services and stick to cheap stuff because it will get ruined.