How fine of a stone?

I think it depends on what you're going after. With my kitchen knives I usually just use the medium then fine and that gets them sharp enough to shave onion slices you can see through.
I have one hunting knife I really wanted to go to town on, so I flattened out the bevel to 17° and polished it all the way down to the sapphire stone, which is supposed to be finer than the ultra fine. It's not quite a mirror edge but it's sharp enough to shave with. It's not really the best edge for a utility knife but it should work for skinning. If I ever get a deer. [emoji]128516[/emoji]

I have used the lansky quite a bit. Like Md I rarely used the course stone. Used medium to flatten out the bevel. Then fine to polish at the same angle. If you really want it shaving sharp use the ultra fine at one step steeper angle and give it about 3-4 good hard strokes per side. This will polish the edge and knock the burr off. Then be sure to warn whoever you hand the knife too. I also picked up a course diamond stone. Works good for refurbishing abused knives or resetting your angle.

As far as knives go, your edge depends on how you want to cut. For meat cutting, say field dressing or post processing, an edge with a little tooth is best. I call it micro serrated. I go to 600 grit, then buff on a bench grinder with white diamond paste (you can get a cheep cloth wheel, and a block of rouge for under $15 at places like Princess Auto, or even Harbor Freight) For cleanly cut meats, say slicing fish or bacon nice and thin, I run the gamut and finish on leather with .5 micron diamond spray.

Next consideration is budget. A Lansky is great for shorter blades, a bit of a pain on say a 14" slicer. Other guided sharpeners like the Edge Pro Apex, or Pro model, out fitted with stones, can run from a couple hundred bucks to several thousand. Then there are individual stones. I have quite a few ranging from $50 to one of my Japanese stones that sells for $1200 (I didn't pay that for it, it was part of a trade)

I have also found rocks in the wild, and sharpened to a very serviceable edge quickly. There is a guy I know (knifemaker) who sharpened a knife on a concrete block, stropped on cardboard and procedes to shave with it. Another video, he shaves with a sharpened spoon. 

Do you prefer a guided system, free hand? what type of cutting? A pirce of 600 grit wet/dry sandpaper on a piece of oak trim, with a piece of leather (old belt) glued on the other side, can strop a knifes edge to shaving sharp in a few passes.

Well, the old adage, "you can get by with what you have" and "you get what you pay for" are both correct. I used the lansky system for a good while when  I started making knives. Worked great on stuff up to say a 6" blade. Then you were forced to move the clamp. I had the stone set, and a diamond set, ended up gifting them to friends and family. Now I use a 2' X 72" belt grinder. I wouldn't personally use any stone finer than a fine. I had the super fine, and still really want a sapphire! Just because.

For general kitchen/butchery chores, going to the N-th degree, to a super fine polish is a waste of time. The edge won't last more than a couple days in any knife of moderate quality. The steels in most supermarket/hardware store knives, are not going to support a super fine slicing edge. Then is the Boss or SWMBO, using them on glass cutting boards, or some other wonder board that was on sale. Typical knives edges dull, not from chipping or having the edge abrade, but from deforming or rolling. Thus the steel! Most people think they sharpen, but their sole purpose is to realign a knifes edge. That's why butchers or chefs seem to be always steeling. At some point they either sharpen themselves, or send the knives out to be sharpened. You can only sharpen by removing metal. The exception to the steel, are ceramic, or borosilicate rods. They are abrasive.

The Apex, is a very capable system, capable of producing exceptionally good edges. It is essentially the same idea as a Lansky, a mechanical guide, holds the stones at a desired angle, the blade rests on the frame, and you sharpen bu moving the stone over the edge. The guide arms are nice and long, so a 10-12" blade is a no issue chore. The basic it will suit most average knife users, and can be tuned with all the top of the line synthetic, and Japanese natural stones, piece by piece, or the set can be purchased all at once. At some point, I will get one, hand sharpening is still my preferred method. These days I opt for speed, and go from cant cut butter, to shaving sharp in about 3 minutes.

I can't say what his source of information is, not am I wanting to discount them. Seki City is responsible for a lot of the Japanese steels. But a lot of the steels use for knives like Henkels, and a couple other makes, use steels from Germany and, Sweden for example. Admiral and Niagra speciality steels in the US, are sources for steels as well. A lot of knife companies will use steels based on the properties the advertise. There are knives made in Japan, that are proud to use Swedish steels, the French Also make a famous line if knives called Sabitier.

I explain knife companies like this: any business exists to make money, and have return customers. In this day and age, we (custom makers and commercial companies) have access to the same steels. Custom makers use the best steels they can, with the best heat treat they can, to produce a product that out performs just about any major knife mass produced. A company uses the same steel, with a decent heat treat, packaged nicely for a reasonable price. Most people buying a $150 chef knife has an expectation of a level of performance. It is better than the Walmart special, looks better, holds an edge better, so when it wears and the end user isn't skilled to re sharpen it, they buy the same knife/brand. That company stays in business, sells more knives, gets some word of mouth advertising, life is good.

As far a single mill goes, they can make a lot of steels, but there are many mills, making a lot of cutlery steels all over the world. Similar chemical compositions in various companies can be similar or even exact, for example, ATS34, CPM154, 154CM are all improvements on 440C, and not dissimilar. RWL 34 is essentially the same steel, but made by Udderholm in Sweden. Ats34 is made by Hitachi in Japan, CPM 154 is a powder metallurgy process whose traditionally smelted cousin is 154 CM, both made by Crucible steel, now Niagara Specialty steels in the USA.

I think you will really be pleased. There is a bit of a learning curve, but there are several videos on youtube that show how to properly index your knife, as well, there are a few modifications you can make if you like to tinker, and squeeze precision out of it. one is with a drill stop collar, the other is an angle cube. Look them up.

Which stones come with it?

Once you get the hang of it, you may want a couple extra stones. 2000, 5000, 8000 ish. You know, for special occasion sharpening! Haha! And because boys wanna see just how sharp, sharp is!! The women in our life may disapprove, my wifes dish cloths are more than well ventilated!

8000 is a good finishing stone for a really keen edge, on a harder steel. I have stones in the range of 25000 grit! If I stone sharpen, I will start at 500 to set bevels, then 1200, 2000 to refine then up to a 5000 Chosera and a 8000 King stone. I have several other stones specifically for straight razors.

20* per side? Hmmm. Tell her they can be a lot better cutters by changing the angle. Start coarse, reset the bevel to the new angle, keep going till you raise a burr on the other side evenly, then progress through your grits using less and less pressure as you go. Before your finishing stone, draw the edge lightly through a piece of softwood, or preferably a rubber wine cork. That will remove the burr. Then finish "strop" with your finest stone.

Look for a video on YouTube for the AngleCube with the edge pro. All this depends of course, on how far you want to push "sharp" and how precise you want to hold your angles.