I wrote a huge response to your question, including a lot of "materials" science and engineering, but the computer gods decided it wasn't to be. I didn't have the heart to rewrite it yesterday, but here's the "Reader's Digest" version.
In discussing "materials" there's a distinction made between strength and toughness. Strength is the quality of resisting bending; toughness of resisting breaking or tearing. They're related which you can see if they're described reciprocally. That is, a strong metal will break or tear before it bends, while a tough metal will bend before it breaks or tears.
Hardness is a quality so related to strength that serves fairly well as a metaphor. There are three kinds of hardness, scratch, rebound and iindentation. Of those three scratch and rebound are directly related to knife performance, especially edge characteristics. Unfortunately, only indentation hardness is usually measured and published -- as Rockwell hardness.
Knives made from tough alloys wear slowly but deform easily. They don't need to be sharpened very often, but do require frequent steeling. Most stainless, European and American made knives fit into this category.
Strong alloys resist deformation but do wear. Although even very acute edges don't bend easily, they do bend and require truing. Some of them are too hard and/or sharpened too asymmetrically to steel at all. As a class, they also need regular sharpening. Fortunately, even a relatively brief "touch up" on a fine stone will retrue the blade as well as freshen the edge.
Actual construction and edge geometries also effect knife maintenance. There are certainly some rules, but nothing beats experience.
Better European and American made, stainless knives (which I'm going to go call "Euro stainless") are almost always made from an alloy called X50CrMoV15, or one very much like it. They are hardened in the range of 54-56HrC, but sophisticated hardening processes. Edge geometry is 50/50 15* flat bevel (or very close). These are forged knives. Forged, western made knives tend to be very thick.
For reasons mostly related to abrasion resistance (largely a function of the toughness/strength levels and balance), at the coarse grits, Euro stainless knives sharpen slightly more efficiently on certain types of silicon carbide and aluminum oxide oilstones than waterstones. Furthermore, because high quality stones of these types -- notably Norton Crystolon (SiC), and Norton India (AlO) are both relatively inexpensive and so easy to maintain, they are the obvious choice compare to waterstone for coarse work.
Euro stainless scratch hardness is quite low. Although they polish beautifully, and German knives especially are objects of gleaming perfection, the actual working edge won't hold a high degree of polish through much work. Consequently, polshing with very fine grit stones is something of a waste of time.
The most common oilstones used for fine sharpening and polishing kitchen knives in the US are called Arkansas stones. In my opinion, Arkansas stones have better synergy following up manmade oilstones than do even very good waterstones. Waterstones are "faster" (it's actually a technical term, but just hold on to the common meaning for now) and are available in just about any grit you desire. On the other hand, Arks don't require any regular maintenance other than cleaning. When you add everything up, if you're going to have oilstones in your kit at all, you might as well complete it with one or two Arkansas stones.
Arks come in five grades. From coarsest to finest they are: Washita; Soft; Hard; Black; and Translucent. Well, sort of. The abrasive in Arkansas stones is something called novaculite, and novaculite crystals only come in one size. So when I said "coarsest to finest," I meant "act like" rather than actually are. Also, because these are (a) natural stones, (b) because most of the good deposits are played out, (c) most of the best stones are long gone, and (d) for a lot of other reasons I can't articulate or think of... there's a lot of overlap from quarry to quarry, from vein to vein and even from stone to stone.
Washitas -- especially "Lily White Washitas" -- just don't come around anymore. Too bad, they were as close you could come to a single stone solution as ever there was.
The best black Arks are pretty much a thing of the past as well, especially from Norton's quarries. "Pretty much" being highly operative, because Hall's Proedge is mining some incredibly good "surgical black" stones. As far as I'm concerned they're as good as a translucent.
Without getting into quarries and qualities let's talk about soft and hard a little. Within the context of an oilstone set, these stones are extremely useful for "chasing" (i.e., refining) a burr. That means you use the stone to make the burr extremely thin at the point where it will be broken off and create the new edge, and to polish the bevel above that point. Consequently, when the edge is deburred, it will itself be very sharp and fine (free from tooth).
Everything else being equal, and assuming consistent grading, a soft is considerably faster than a hard. If you're going to go on to a finer stone -- whether black or translucent -- a soft is a fine platform. If on the other hand you're going to stop at this stage because you don't want to a very fine polish on the edge, it makes sense to skip the soft and go to the hard -- which will produce a finer but still workable polish than the soft would on its own.
So, do you want to stop with a hard Ark or is it worth investing in a soft and a black?
If it's all about practical sharpness and economy, stop with the hard. If you're someone who loves tools, fooling around with hardware, doing the best possible job regardles, and so on... you might as well bite the bullet and go with the soft and black stones. The Hall's Proedge black is a real standout compared to what else is available, and their soft is good enough that it's not worth buying from anyone else.
Lower cost, stamped knives tend to relatively thin. Forschner Fibrox and Rosewood split the diff, in that they are stamped, but made with the same alloy hardened in the same way. F. Dick Eurocuts, too. Because of their thinness, they sharpen faster than their betters, and act sharper longer; although they need just as much truing on a rod-hone (steel). I'm not sure why, but they tend to hold polish longer as well.
Now, when it comes to non-stainless (what knife guys call "carbon") and the stainless alloys employed by better Japanese knife makers, oilstones won't do the job. You need waterstones. Since we're not there yet, I won't go into the ins and outs.
Okay, "need" is relative. I certainly sharpened a lot of hard Japanese knives on oilstones. But, it's slow and annoying. And slow has consequences. Slow means more strokes to do the same work and more strokes multiply the possiblity of error. So, slow stones put a premium on technique. Faster stones are better for everyone, but much better for beginners.
Also, you can do a perfectly fine job on good Euro carbons (e.g., Sabatier carbons) with oilstones. Perfectly fine, but not as good as with waterstones. Years ago, I used to sharpen my Sabs up to a Norton translucent, and until recently I went with a Hall's surgical black. But the Naniwa SS 8K (waterstone) does a much, much better finish. No comparison really. What else can I say?
As to integrating waterstone and oilstones into a single kit. You can, but with a lot of caveats. If you use oil or soap on your oilstones you don't want your waterstones anywhere near them. Oil will wreck a waterstone. While soap isn't nearly as bad it's not a good thing either. For whatever reasons, an Ark is a better follow up to an India than any waterstone.
Then, once you've switched to a natural stone you don't want to follow up with a manmade. By virtue of their inconsistencies natural stones create complex surfaces that are very advantageous in terms of actual use. You don't want to lose that by switching to a synthetic waterstone simply to gain speed, save money, or simplify your kit.
Speaking of money, coarse stones, even most of the best coarse waterstones, are not very expensive. And, as long as you stay away from the translucents, Arks aren't terribly expensive either. It's the finishing quality waterstones that are going to hurt -- and you don't need one for your current knives.
Swarf... Right in one -- pretty much. Swarf is the metal filings which come off the knife during the sharpening process. Slurry is the mix of binder, friable abrasive which comes off the stone during prep or sharpening and mixes with the sharpening liquid (if you use one). Slurry mixes with swarf. If it aids in sharpening, it's still slurry. If it's climbing up the side of your knife and making scratches it's swarf.
BDL