We've had mostly discussion of "brands" here, but little comment about the particular styles people like. I do have one of those "Japanese" (probably about like the "Chinese" that petr mentioned) cooking knives, and use it quite a lot. I got mine from a little "generic oriental" shop in Seattle quite a few years ago. Mine is marked "Pilot - Sakei Japan" and my recollection is that I paid about $20 (US) for it, maybe 15 years ago. I've tried a couple of cheaper similar ones, but wasn't much pleased with them.

It's pretty much standard to have one good "butcher knife" about 8 or 10 inches long. This one has a slightly curved cutting edge, about 1.5 inches deep at the "fat" end, and should have a thick enough backbone to "spread" the meat for thick cuts. If there's one knife in your "kit" that it's worth spending a little extra on, this would probably be "the one." My current one is a KC Cutlery, although I have a Trident/Wusthoff in backup. A good one will probably run around $30 - $40 (US) in my local shops, although you can go close to $200 for some of the "exotic" ones. My recollection is that the Trident had a "list price" of about $135, but of course you don't pay list for them.

Less used, perhaps, but handy is a "slicer." Some people call it the "ham knife," and it gets used mostly for slicing thin slabs off the Christmas ham or turkey. Straight edge, usually 8 to 10 inches long, and about 3/4 inch deep blade. Because it's often used in front of the guests, many people opt for a "pretty" one, and as long as it holds a decent edge I wouldn't fuss too much about having a particularly expensive one. The "Waverly Edge" (scalloped) is common here, and is probably ok, given the limited use by most people.

Every cook needs at least one "French Chef." I personally prefer a shorter one, about 8 inch, but 10 inch and larger are popular. Most of the "class" ones are a fairly heavy blade. Some people prefer something a little lighter. While the bigger ones are "impressive," your choice should depend on how large a workspace you have. For most home kitchens the larger ones are a little too much. This is one you have to try it out to find what suits you. I use mostly my KC here too. It - or the "Chinese" - are what you use for mincing and dicing.

Many "sets" include a Cleaver, but for home use I find they mostly just sit in the block. It's usually better to "find the joint" and cut it with a knife than to "hack through" - at least for the stuff you're likely to deal with unless you're starting with "live meat on the hoof."

At least one decent "Boning Knife" is a good addition. This one should have a fairly "slim" blade, but not too flexible. It's the one for getting the last bit of meat off the turkey carcass, and for general purpose with smaller jobs that don't quite need the butcher knife. About a 7 inch long blade is pretty typical.

The only "serrated blade" I use, only loosely called a knife, is the "Bread Slicer." With the hard crusts "She" bakes, you do need a little "tooth" to get through the crust without crushing the loaf. I use a $9 one that lives in the bread box (so the real knives won't be offended).

Smaller utility knives are generally cheap enough that you can try out a few and settle on what suits you. Paring knives, etc come in remarkable variety, but a few reasonably good 3 inch paring knives, a "hook blade" parer or two if you like them, and perhaps a couple of slightly larger "utility" kind should equip most people for doing what needs to be done in the kitchen.

In the "utility" group, some may want a "Filet knife," but for most that one belongs with the fishing tackle. It looks similar to the boning knife, but has a very flexible blade, for "following the skin" when you filet your fish. (Often with an assymetrical edge, too.) Not needed by most people in the kitchen, but suit yourself.

I use a couple of "utility knives" that are converted from "steak knives" of the sort you see in some "class" steakhouses. The came with serrated blades, large handles, 6 inch or so long x about 1.3 deep blades, and with the "teeth" ground off they make a very nice utility knife - for about $3 (US) each. With the teeth left on, I'd consider them a "throw-away." Very handy, after conversion, for camp cooking, since they are about right to replace the paring knife and a larger utility size almost up to butcher knife scale.

Of course, everyone should have - and learn to use - a good "Steel."

And no "gentleman" is properly dressed without a serviceable pocket knife.

John