There is nothing else in your kitchen that will get used as much as your basic three knives so don't skimp. I'm going to sound like a bit of a snob but if its being shilled by some greasy brit on late night TV then its a piece of shit. If it comes with a bonus of a fold flat colander, pasta scoop, ice cream maker or any other useless kitchen gadget then its a piece of shit. If you can buy a basic set (small paring knife, medium paring knife an a chef's knife) for under $50 they're a piece of shit, under $100 they're a piece of crap, under $150 you're getting close.
If you're operating on a budget you'll only need three knives. First, find the highest quality 8" chef's knife (or santuku, I actually prefer this style of knife given its straighter blade) that you can afford that feels natural and balanced in your hand. Handle shouldn't be too big or too small and you should be able to weld the knife we ease but still feel as though there's something of substance in your hand. After you've spent the bulk of your coin on a good chef's knife find a 4"-5" paring knife. Definitely look for something decent quality but since this knife will likely face a fair bit of abuse, and consequently shorter life, you don't need to go as high end. Find something that holds its edge, feels sturdy and again has a good handle as you're going to use it for coring, peeling, etc. Lastly find a cheap chef's knife that you can abuse without remorse. Find something with a molded plastic handle with a nice roughed up finish that you can hold onto if its wet or greasy.
Once you've got the knifes treat them well and use them as they were intended. Despite what you may have seen in those shitty infomercials don't use the knife to cut pipe, leather, rope, wire, tin cans, etc. I have an ex GF who seemed to think her kitchen knife was the household multitool. She'd use it as a screwdriver, can opener, stir stick....aside from bugging the hell out of me its just not safe. Next, keep the blades sharp! Knives, like people, get dull and need proper up keep. Sharpening the blades requires a bit of science and IMO something like
this kit from MEC is perfect. Provides you everything you'll need to keep the blades sharp and your fingers safer. Once every few years, or if you get a major knick in the blade, take your knives to a proper knife smith and have them re-profile the blade. Don't bother taking in your cheap chef's knife as replacing it will likely be less expensive. When not in use don't just throw them into your kitchen drawer. If you don't have the space or need for a knife's block then just get a couple of blade guards (just a little piece of plastic to slip over the edge) when they're not in use.
As you budget grows you can expand your collection. Some suggestions would be a carving knife, bread knife or cleaver.
Happy cutting!