Kitchen knife has to be sharp and hold the edge well. It should be the right size and weight. Smooth blade can be sharpened, serrated blade is not meant to.
Kitchen knives are all knives used around the kitchen. They vary in weight, length, shape, and edge type. I'm no chef, but I cook a lot, and have my strong preferences. Basically, I use two knives: a chef's knife with a 9" blade and a 3" paring knife, both made by Global. I use a third one, 7" cheap thin stainless steel utility knife, when I risk to damage the blade, for example to cut across the joint when quartering a chicken.
Global chef's knife is a cross between traditional French chef's knife and Japanese santoku knife. It is lighter than a French knife, with relatively thin steel handle with small black-dot indentations for grip, and made in one piece with the blade. The blade curves upward slightly, it has a fine point and a triangular profile with acute bevel angle. It is made of hard high-chromium stainless steel -- again, a cross between hard and sharp carbon-steel knives and easy-to-care-for stainless steel. It stays very sharp with normal use, but requires careful sharpening. Global sells MinoSharp Water Sharpener with two ceramic sharpening wheels, coarse and medium. The angle of wheels make them not suitable for one-sided cutting edges and not recommended for blunter bevel angle. I used it to sharpen my utility knife I don't care much for anyway. However, if you want to make best use of your razor-sharp, lightweight and controllable Global knife, sharpen it with whetstones. It takes time and care. I learned how to do it but don't trust myself -- it's my husband's real man's task. Kitchen knives are not dishwasher-safe: high temperature loosens the steel and bumping into cutlery damages the edge. Detergents are corrosive. There are blocks, plastic sleeves, and magnetic strips to store the knife. I don't use any, but make sure my knives don't touch anything and never put them in cutlery cabinets or in the sink with the dishes. The last one is a good safety measure: imagine grabbing the blade in the dirty soapy water. A good place for the main kitchen knife is on the wooden cutting board.
Traditional European knives are never as sharp but not as easy to damage, also easier to sharpen because of softer steel. Sabatier is most prominent expensive French brand and Wusthof Dreizack by Solingen is German. I never had a good Solingen knife. Their small cheap knives are nothing special.
Besides smooth blades, people sometimes use serrated knives. Serrated knives are not meant to be sharpened. They are cheaper than smooth knives and basically are disposable. Serrated knives are supposedly good for bread or tomato -- something much softer inside than outside. I don't have a serrated knife and prefer to keep my knives sharp enough to cut tomatoes. Another bad idea is set of knives, sometimes sold with a block to store them. Knives from the large set never get sharpened, and wooden blocks get filthy. Sets and blocks are usually "affordable", which means inferior steel. Get one good knife for the price of the set.
See also: kitchen, knife sharpening, frying pan, stand mixer, coffee grinder.