There are a lot of knife threads here and some tutorials. Have you perused the kitchen knife section here? It's a little hard to know what to suggest without knowing your style and how you use a knife. I like knives that are light and thin, and I like very little belly (that is, a knife with a straighter edge). I like high carbon steels and tools steels and am not a big fan of the more popular stainless steels like VG10.
You could spend months getting a handle on the basics! In broad terms there are two kinds of Japanese knives, traditional and western. Speaking in generalities traditional knives are single beveled and western types are double beveled. The former are designed for preparation of Japanese foods, and there are many of them for different kinds of seafood. Western knives are patterned on French and other European knives. Most of us that are into Japanese knives will be using Western style J-knives.
The Shun that you linked in another thread is a Western knife in the Yo style. Wa handles are the round, D-shaped or octagonal wood handles that affix to the rattail tangs of Wa-style knives. Yo-style feature scales affixed to a full tang in the manner of European knives.
Broadly speaking steels fall into two categories: High Carbon and Stainless. HC knives will (generally) take a better edge but will stain or rust. SS is carbon steel with other elements added to give certain properties, like corrosion resistance, toughness, edge stability, etc. Among HC steels White #1 is probably the purest and takes the best edge. Ao-Ko/Aogami has added tungsten for toughness. It will get almost as sharp and hold the edge longer. 52100 is an American HC steel that rivals White #2. The "purer" he steel (ie the less stuff added to it) the smaller the carbides generally are. Without going into materials science, finer grain structure means the knife can be made sharper.
Tool steels and some of the "Super Steels" can't be completely categorized. Some tool steels get almost as sharp as HC while being pretty resistant to corrosion.
"Damascus" is often referred to as suminigashi among Japanese makes (suminigashi means "ink"). In 99% of the knives you see it's just a decorative cladding that does nothing for performance. I would avoid it unless you simply can't live without the look. The hagane (or core steel) is the important part. The jigane (the cladding) just protects the core from corrosion and damage.
A knife made of one kind of steel with no cladding is often called 'monosteel'. In a traditional knife made by hand it might also be called honyaki (loosely true forged). A knife made with an inner hagane and outer jigane might be called san mai, kasumi or by other names, depending. Just bear in mind that the jigane is normally just decorative. Don't get hung up on it. You may see suminigashi or just plain stainless; in a rustic kuroichi pattern there is "flash" on the blade that serves the same function.
Again, in broad terms a thin, light HC blade (often called a laser) will offer spectacular cutting performance but you'll have to take care of it. Something like White #1 has to be babied a bit. Like a Gremlin you want to keep it dry and don't feed it after midnight. Okay, just keep it dry.
Stainless if a bit more forgiving and easier to live with day to day but generally won't get as sharp.