I'm of the opinion that geometry and heat treatment is a little more important than specific steel choices. The biggest decision on steel for the kitchen is whether to go stainless or not. If everybody who is expected to use the knives is willing to do the little bit extra to care for a non-stainless carbon steel knife, I prefer it because it can get screaming sharp with little effort. Even when it loses that scary sharp edge, it can often be brought back with simple stropping; I usually just strop on newspaper laid on the kitchen counter.
I'll still geek out a bit on the steels... a lot of people feel for stainless AEB-L with good heat treat will have finer carbides and can sharpen easier than some other stainless. If the maker is good, I still think all the common kitchen cutlery stainless can work well. For regular carbon steels, the higher alloy steels can offer better abrasion resistance, so you can slice longer between sharpenings. But I'm happy with simple carbon steels as I mentioned it's simple to strop back to razor sharp as well as easily sharpened when need be.
A heavy meat cleaver is best for chopping bones and frozen stuff, something with some spine width and larger obtuse edge angle that will hold up to abuse. Not too hard, better for the edge to roll over and be steeled back than to knock out a huge chip.
For veggie prep and boneless meat, it's nice to keep it simple with a do it all type chef's knife or the Japanese equivalent, the gyuto which is partially modeled after a French chef's knife anyhow. For that, I prefer a higher hardness blade, Rockwell HRc of 60 or more that can take a fairly acute edge angle, between 10 to 18 degrees per side, depending on the maker, the geometry, steel and heat treat.
Everybody is different, some people like a long chef's knife like 8 to 10 inches of blade, others a smaller knife like 5 to 7 inches. If you use a pinch grip, it's nice to have the spine rounded but for home use, I can usually get by without since I'm not cutting for hours like a restaurant kitchen professional. Handle preference is also very personal, both shape and material. I prefer real wood or stabilized wood over man made stuff like G10, micarta, etcetera. But the man made stuff will be safer to wash and not experience movement in service or even due to changes in humidity that can cause wood to swell and shrink.