I will second what Rick says. Knife sets get zero respect on this forum.
Also, the Wusthof Classic Ikon knives, while just about as good in quality as anything else mass produced in Europe, just don't cut it in terms of quality when compared with even basic good quality Japanese knives, such as the Tojiro DP knives.
However, the good thing here is that you're talking about a respectable amount of money - $860. With that as a budget, let's see what would be an idealized purchase (at least as I would spend $860 on a desert island set up)
First, it's not just about the knives - it's also about the rest of the gear that makes and keeps the knives sharp. And it's also about a good cutting board. You're going to need that to slow down the inevitable dulling that all knives get in use.
So, a few assumptions on my part. First, I am assuming you are in the USA. I have to make that assumption because availability and cost of virtually (almost) everything is dependent on where the person lives. Also, it's easier to make my case if I'm only dealing in the U.S. dollar.
I'm also going to assume you want a stainless knife, rather than a carbon steel knife.
Of course, if either assumption above is different from reality, then please let us know.
So, I'm going to divide the purchases into three broad categories - (1) knives, (2) sharpening equipment and (3) cutting board. And in each category, there will be the BIG purchase item and there will be the small change items. So, here goes...
KNIVES - In truth, three knives should do (almost) everything. The work horse will be the chef's knife. Then, there's the fine detail knife - the paring knife. And there's a specialty knife - a serrated edge bread knife.
The Big Kahuna here is the chef's knife.. In the Wusthof set, that chef's knife is 8 inches long. That's just too short. You really want something a bit longer, say 9-1/2 inches to 10-2/3 inches. In metric terms, 240 mm to 270 mm. And, that the length of the blade. Shorter than that, and you will find it hard to effectively carve up a roast.
I'm just going to drop a single manufacturer, series, type and length here - the MAC Professional 9-1/2 inch Chef's Knife (MBK-95). This is a workhorse knife which is used by top chefs the world over. Yes, there are better knives. Yes, there are less expensive knives. But this is probably just about the single most widely known knife in the profession world-wide (Kiwi knives excepted), and is a safe flat-out recommendation. List price is $220, and you can buy it from various eBay sellers for $184.95, including shipping. When in stock, it's also available from Chef Knives To Go ("CKTG"), an on-line retailer, for that same $184.95 price.
Other knives which have come up have been the Masamoto VG 240 mm gyuto ($197 at CKTG). Also, the Hiromoto 240 mm AUS-10 240 mm gyuto is available from japanesechefsknife.com (a web site based in Seki City, Japan) for $110 plus $7 shipping world-wide. And I'm sure other knives will pop up as well with the development of this forum thread.
Now for the paring knife. You can either go with the usual Victorinox fibrox handled spear-point for about $7 on eBay, or you might also consider the MAC Professional 3-1/4 inch paring knife (PKF-30). It's about as short a paring knife as available, it's (at least for me) just about the length of my index finger and that's just the length that allows my hand to think of it as a sharp version of my index finger. Retail list price is $70, most eBay sellers and CKTG sell it new at $59.95.
For a serrated edge knife, I would just suggest you go to a commercial kitchen supply shop and buy a molded handle serrated bread knife. Victorinox is usually the better brand, but Dexter will also do. If you can find it cheaply get one at least 10 inches in length. You don't want to spend too much, because sharpening these is a real PITA. Usually, chefs just throw out the old one and buy a new one, rather than try to sharpen it.
Even if you don't eat or serve bread, a serrated edge knife is the best knife for such tough skin but soft interior foods as tomatoes. For that type of job, it's better than your trusty chef's knife.
At this point, let's do a price check and see our budget. MAC MBK-95, $185. MAC PKF-30 - $60. Bread knife, $25? Total is mebbe $270. That leaves $590, more or less.
SHARPENING - The reason this is essential is very simple. ALL knives get dull with use. Period.
For general quick maintenance of your chef's knife, a good quality honing rod is a godsend. It won't sharpen the knife edge, but it will microscopically re-align the edge. And the best available is the Idahone. Get the 12 inch length from CKTG at $32. And then either pound in a nail somewhere in the kitchen to hang it on, or get a hook and tape from your local general goods store. They are sold as the 3M "Command" system. About $5. Well worth it, since the Idahone is a ceramic rod and will shatter when dropped.
For sharpening, you can get several water stones (500 grit coarse repair stone; 800 to 1200 grit medium stone and 3000 on up fine stone). CKTG sells a good set of a Beston 500 stone, a Bester 1200 stone and a Suehiro Rika 5K stone, with a 20X magnifier and deburring block for $139.95. Then watch Jon Broida's sharpening videos at JapaneseKnifeImports.com.
Or, for a much quicker learning curve, get CKTG's "Edge Pro Shapton Glass Stone Set" at $339. Well worth it. You will be sharpening your knives with excellent edges by yourself faster than any other method.
Let's check our budget again. Idahone, $32. (I will assume you have a hammer and nail around somewhere). Edge Pro Shapton Glass Stone Set, $339. Total, $371. That leaves $219, more or less.
CUTTING BOARD - Use a bad cutting surface and you risk prematurely dulling the blade or chipping the edge. The best boards are end grain hardwood boards. And the standard wood most commonly used is hard northern maple. The basic minimum size is 2 inches thick by 12 inches by 18 inches. And yes, larger can be better here.
One of the best makers of boards is The BoardSMITH. his board can be works of art. And here, a bit of splash may just be the thing to liven up your kitchen. Consider a 2" x 12" x 18" Maple/Walnut Border board for $168.20. Yes, a bit of splurge might be warranted. Or, if practicality rears its ugly head, a 2" x 16" x 22" maple-only board will run $196.75. Not as much dazzle for the eye, but a larger cutting surface and more space to use for those big family dinners.
When ordering from him, keep in mind that communications is vital here. What you order will be what he makes. If you do or do not want feet, make absolutely sure that he and you agree ahead of time on what will be ordered. Personally, for me that means no feet, so I can reverse the board from time to time. But, it's up to you. Also, check with him about shipping costs. I didn't see that on the web site.
You will also need to treat the board. I use food-grade mineral oil from a big box food chain for $3.49 for 16 fl. oz. And I really slather it on, multiple times, until the board just won't let any more soak in.
You also need a scraper to scrape the board clean. I buy mine at an off-price store for $3.
Well, that's my fantasy for $860. And with the fancier (but smaller) cutting board, I will have spent about $816, leaving me with about $44.
How does that sound?