Not many things are more upsetting to me than being asked to cook in some one else's kitchen, only to discover that the only knives they own are either so dull I'd be better off using a bowling ball to cut things, or they're all of the "never needs sharpening" variety.
First of all, The most frequent cause of accidental cuts is a dull knife. Picture trying to cut a tomato, pepper, or anything that has a round surface and thick smooth skin with a dull knife - the blade slips off and you spend the rest of the afternoon in a clinic getting stitches. If you're gonna have real knives, go get yourself a medium or fine grit sharpening stone and a honing rod (and no, a honing rod does not sharpen the knife, rather it just "hones" the edge, once it's dull it's dull, get a stone too). Both are relatively inexpensive. And PLEASE do not keep them knocking around in a "knife drawer"... there's no better way to take the edge off of a good knife than to leave it rattling around in a drawer with other metal objects. Get yourself a magnetic strip, a knife block, or rack to hold them safely away from each other and from damage.
Secondly, the only knives in your kitchen that need to be serrated are a bread knife and steak knives for your table setting. Those incredible things that you bought for convenience are nearly useless in my eyes; they're better at tearing through foods than actually cutting them.
If you're looking to upgrade or re-stock your collection, here are a few tips to help you along:
Most companies that make the knives professionals use also make cheaper models most people can afford, and they're a hell of a lot better than any
Henkels chefs knife
"bargain knife set" you might see on TV or in a store. The top 2 companies most pros go with are Henkels or Wusthof (also known as Trident). I personally use mostly Henkels. However, they don't hold an edge as well as a Wusthof, so they require frequent maintenance, but they are heavier and made of harder metal. Wusthof is the most common brand seen in a chefs knife kit for these reasons, but I still like, no love, my Henkels. Another common brand in restaurant kitchens is Forschner. Much less expensive than the other two, so they might be a better choice for your daily home uses. You really do get what you pay for here, though, so realize that lower price tag means lower quality as well.
Selecting which knives to purchase can be a daunting task when faced with the near endless multitude of blade shapes and sizes. The truth is, all you really need as a home cook is one good chefs knife. Maybe a paring knife and a slicer as well, and perhaps a boning knife, but as long as you have one good chefs knife it's all you're really gonna need. It's the backbone and workhorse of any good collection. The width of the blade makes it good for chopping, the length makes it good for slicing, the curve makes it good for fine work like small dice, and the weight makes it a decent cleaver. The tapered point is also good for detailed work.
If you do a lot of roasts or other large hunks o meat or fish you might also want to invest in a slicer. The longer blade means one swipe, clean slices without having to saw through things leaving jagged edges, and the thinner blade will give you less friction meaning it will pass through much easier.
Paring knives are good for small detail and decorative cuts, and boning knives are just that, made for de-boning meats and fish. They are also good for smaller vegetables. However, these knives are probably not gonna be used very often by the home cook, so it's really up to you whether or not to spend the money on them.