So, I'm a line cook in a fairly high volume restaurant. I'm currently building a knife set, and I'm considering adding a carbon chefs knife to the range, probably a carbonext.
A CarboNext is not a "carbon," it's "semi-stainless" and more stainless than semi.
I'm just wondering how much care I'd actually have to give the knife, while on the line. Is there a significant amount of care, or is it just giving it a wash and a dry every time I use the knife? When on the line, will the extra sharpness I gain from having a carbon, outweigh the troubles caused by it?
Carbons are are more demanding than needy. They don't require much extra care; rather they require their care RIGHT NOW.
You don't get much extra sharpness anymore from carbon as opposed to the really good semi and stainless alloys. And, don't forget, if you want to exploit what difference there is you'd better be a very good sharpener. Carbon alloys typically feel better on the stones than their more stain resistant counterparts; and may get sharp a little faster. Plus, not all carbon alloys are created equal.
I used nothing but carbon during my short career on restaurant lines (at a time when carbon was still hugely superior in most ways) and didn't find their care particularly onerous.
It's best to look at the problem as whether a specific knife is worth pausing for frequent wipe downs; and many certainly are. Word to the wise though, don't go carbon with your citrus knife.
I'm also considering getting a Richmond, either an Artifex or Addict. Is there a significant difference in the knives or is it mostly the handle?
Yes they're different. The Addict is more refined in a lot of ways, while the Artifex is huge bang for the buck. If I could afford them equally, I'd probably base my choice on profile and appearance; but can't tell you which you'd like better. A fair comparison would be looking at the differences between a Wusthof Classic and a Forschner Rosewood.
Call Mark Richmond (at CKtG) and talk to him. It's not an imposition, he loves to talk to customers.
One last thing, I'm also getting my first stone soon. I've previously been sharpening on sandpaper, but as I'm using the knives more now I'm willing to spend the extra on a stone. How long would a stone usually last? What grit(s) should I get?
It depends on how many knives; how often; how you maintain; how much money you're willing to spend; and whether you consider the extra cost and harder feel of longer lasting stones worth the price. Grit is often a big factor as well.
If you're a home cook who only sharpens his own knives and doesn't have too many of those -- you could probably get two years out of a King Combi, and a lifetime out of a Gesshin 8K.
Your grit choices depend mostly on what kind of knives you have and what kind of edges you want to create. It also depends on how you view the sharpening processes. I see those as profile/repair, sharpening itself; and final sharpening/polishing -- and view sharpening through the prism of pulling a burr and deburring. Seen that way, you want either a three or four stone kit.
CKtG sells a nice, Japanese synthetic, three stone kit with a little discount attached: Beston 500, Bester 1200 and Suehiro Rika (3K - 5K, depending).
Don't forget that water stones require flattening.
Depending on your knives (and your future plans), your best choice may be "oil" instead of water stones.
Before you get out the credit card, let's talk a little more about what you have, what you're going to have in the foreseeable future, what sort of edges you want, the level of PITA you consider worthwhile, and how much you're willing to spend.