For the moment, skip the entire discussion of profiling. My one objection to that article is that he puts profiling so front and center that you don't realize how rarely you'll ever do it. For your Global, I'd start by using the factory edge, which I believe is about 15 degrees, which is fine. Just put the knife on the stone and lift the spine until the edge just barely bites, and grind there. Eventually, you may want to set a new edge, or you'll want to do it to another knife, and then you can do some profiling, but wait until you have a reasonable familiarity with the basic sharpening process and feel like buying a coarse stone.
Speaking of which...Grits:
Different broad types of stones are graded differently in terms of grits. Japanese waterstones are graded very consistently, and the numbers we've been bandying around refer to their system. The grit refers to the number of little abrasive bits in a given space, just like with sandpaper. Few big grits grind faster and coarser than lots of small grits.
Very roughly speaking, you can divide stones into coarse, medium, and fine.
stone, from about 700 downward, is extremely aggressive and takes off metal rapidly. It will leave a "toothy" edge, meaning that if you look at all closely at the ground metal, you'll see definite scratch-marks, which continue right into the edge itself (though there you need to look through a glass to see them). As a rule, a coarse stone is for fixing things: a new knife may need a new profile, a chip may need to be removed, the edge may need reshaping because of a screwup, whatever. Rarely would you want an edge like this for cutting. Stones like this are cheap to medium-cheap.
stone, from about 800 to 3000, gives a mildly toothy edge. It is aggressive enough that you could
fix a knife with it, but you wouldn't want to -- it takes a long time and a lot of work. The scratches these stones leave are fine enough that you will have to look for them a bit -- they're not obvious, like with a coarse stone. If you've used a coarse stone first, you use the medium stone until all the coarse scratches are gone and all you've got is the medium ones. An edge like this is good for most cutting work, and ideal for the more brutal things. This is because those scratches make the edge just a little bit like a saw, so when you move the edge through the food it chews through. If your knife is in basically decent shape, you start here, not with a coarse stone. Stones like this are usually fairly cheap.
stone, above 3000, essentially polishes out the scratches. At high grits, like 10k, the stone will leave a mirror-like shine, so fine that you have to look under a powerful lens to see any scratches at all. As a rule, stones like this are not very aggressive, and they tend to wear relatively rapidly (see below about this point). An edge like this is primarily desirable when you want extremely smooth, clean cuts. For example, a yanagiba for slicing raw fish into sashimi is normally polished very fine indeed, because you want the fish to be perfectly smooth, and any hint of "toothiness" will tend to catch the flesh and deform the slice. For what you describe, I doubt very much you want an edge like this, though it is worth remarking that Kyoto kaiseki chefs, the unquestioned Japanese masters of vegetable cookery, polish their vegetable knives (usuba) very fine; then again, their cutting techniques are quite different from what almost anyone else does. Fine stones are generally somewhat expensive, and can be very much so.Wear and Flattening
: A synthetic waterstone is essentially a bunch of abrasive grit bound with a glue and baked into a brick. When you sharpen, the grit comes away as a slurry on the surface of the stone. This slurry is essential to the process on a great many stones, and generally leaves a somewhat finer edge quicker than with a less "muddy" stone. But because this slurry is coming off the stone, the stone is getting worn away, and what's more it's becoming uneven. An uneven stone produces poor results for sharpening. Thus you must flatten your stone before using it. There are expensive and cheap options for this. My favorite, and I think BDL's, is a sheet of wet/dry sandpaper laid on a thick piece of glass on a countertop. You take a pencil and make some rough cross-hatching on the stone surface. Then put the stone on the sandpaper and grind around, changing directions and grips often to keep it random, until the pencil marks are gone. If the stone is basically flat to begin with, this won't take long.
Sharpening the same knife every day is almost certainly unnecessary unless you have rotten cutting technique or a terrible knife (which the Global is not).
Based on what you describe as your use pattern, I'd start with a Norton or King 1000 stone, whichever is cheaper. I just googled the King, and found this place
selling them for $24.50. You can probably find it for a little less, but you'll also find places selling them for a lot more -- don't get taken! I have heard good things about the Norton but have not used one. The King, the most popular stone in Japan, is reasonably aggressive, not very muddy, slow to wear, and extremely easy to use. Just drop it in a bucket of water about 20 minutes before you want to use it and you're good to go. The edge you get will be perfectly serviceable by most pro kitchen standards in the West.
I had been recommending the 1k/6k combo stone, but it doesn't sound like you have any need for that kind of polish, so I'd say skip it. If you get to like sharpening, you can always get a 6k later.
Your second stone purchase should certainly be a coarse stone. The common favorite among sharpening mavens appears to be what's called a "pink brick," a very durable 220 stone. Somebody here probably knows the actual brand name of this thing so you can search for it. It will cost about the same as the King. (If you can't find it, let me know and I'll ask somebody where you can get it -- I don't know US retailers because I'm in Japan at the moment.)
If your Global is unusable because it's dull, you can certainly sharpen it on a 1k stone, though it may take a little while the first time. That's OK, though: at this point, you're better off taking longer than using a super-fast stone. That way if you do a stroke really way off, it'll make very little difference; a fast stone can do damage fast. Once the knife is basically OK, you can probably keep the edge sharp with just 5-10 minutes once a week.
Once you get the hang of basic sharpening, which won't take long, set aside 20 minutes every day at the end of work, like you suggested. Sharpening is very meditative and relaxing, so use it. Every day, check your chef's knife to see if it needs work, which it may very well not. If not, go through the rest of your kit. If everything is sharp, put a decent edge on a house knife. In time, you'll get very fast and smooth, and the knives in the kitchen will be getting seriously sharp. If you actually do this every day, in 2 months you will be very, very good at this.
Apparently what usually happens next is that Chef decides maybe you're on to something -- so you should sharpen his knife (he's not going to!). If you're lucky, others in the line may ask you to show them how to do it too, but don't count on it.
By this point you are likely to be something of an addict. Danger! From this point on, sharpening becomes much more fun... and much more expensive. My suggestions for a further stone when you become a nut is a 6k synthetic Arashiyama: very muddy, rather soft, leaves a beautiful edge. It'll cost about $75 or so.
Pretty much the premier synthetic stones now are Naniwa Chocera's, known in Japan as Cho-Ceramics (choseramikusu). They are very expensive, but they produce remarkable results, and are generally agreed to be the most like Japanese natural whetstones of all the synthetics. Natural whetstones can be extraordinarily superior to any synthetic, but you really, really don't want to know what they cost. (Hint: I've seen one for $35,000, no joke.)