Choosing a chinese cleaver/chukabocho fit for a cooking enthusiast
Actual traditional japanese knives are even less "all purpose" than european style knives.

The knives referred to in the question are not japanese but chinese in style. They are commonly manufactured, though, by both the chinese and japanese makers. The japanese call a japanese-made chinese style knife a chukabocho (chuka means "chinese style cuisine", a bocho is a cooking knife); the japanese made knives have a reputation for extremely high quality but are also very expensive (likely because they are marketed at professionals and enthusiasts in japan and the west, not as a common household tool).

There are knives in the (semi) traditional japanese spectrum that look similar, but have about half the blade height: The nakiri and edogata-usuba styles. These are far more delicate knives meant for vegetable work.

Carbon steel or not is something you should discuss with the chef that will use it - some chefs hate the more difficult sharpening and sometimes lower attainable sharpness of stainless steels, some hate the rust proneness of carbon steel. Repeat: carbon steel (as opposed to "high carbon stainless") is GREAT knife steel but it is NOT stainless.

"Forged" or not is more a description of production method sometimes misused for marketing - some carbon steels get metallurgically better when (hand) forged, stainless steels usually do not.

"Composite" probably refers to a japanese-style cladded (Awase) blade - SOME cladded knives have carbon core and stainless cladding, which gives you an easy to sharpen and extremely sharp knife that will have less rust problems (where the core layer is exposed is also where you regularly abrade material when sharpening - so you will take care of actual rust anyway. Patina is not rust!).

For the most universally usable knife, stainless is advantageous if fruits or other sour ingredients are regularly handled.

There are a few important specifications to be aware of with a chinese cleaver (that is what that style of knife is called):


Blade thickness: Most makers (especially the chinese ones) have a variety of differently thick models - this bears more on the weight and handling feel of the knife than on the cutting ability (for which the next point is crucial).
Thickness/Thinness right behind the cutting edge. This can be adjust when sharpening but is a lot of skilled work to adjust. Too thick won't cut well, too thin will be delicate and will take damage if eg hitting bones or hard seeds. Best try the knives in person, and bring some hard root vegetables (anything that can smoothly slice (not split) through a fresh carrot is seriously thin (maybe too thin for a cleaver), if it completely wedges and refuses to go any further it is too thick for a general purpose knife.
Edge profile. Some have a nearly straight edge, some far more curved - this is a matter of user preference (depends on preferred technique). If you see anything with a completely straight edge, you are looking at a specialty knife (like a noodle making knife or a big usuba) that will be very awkward to use for most cooks as a general purpose knife.
Steel and hardness. The gentler your friend handles a knife, the harder a knife you want. Hard means it will stay sharper longer if used carefully, but break or completely dull quicker if abused. The 58HRC quoted on a few of these is a good medium, would be a bit too hard for rough (bone contacting) butchery tasks (which this knife isn't meant for anyway). The 54-55HRC range is best left to actual butchery tools, the 60-63HRC range really requires careful use but can make it through far more work razor sharp. 64+ HRC is not really the hallmark of something "universal".


If you want to make sure you get a knife of known quality, go for a reputable brand - if I may give examples, for that style of knife CCK (Chan Chi Kee) appear to have excellent reputation for chinese (actually hongkong) made ones, for japanese made ones Sugimoto and Moritaka (warning: sticker shock risk.)