Specific brands would be helpful too!
Since you say "a" knife I assume you want the one most useful blade. The most versatile knife for most people would be a chef's knife. Your second blade would probably be a paring knife for fine work. Quality cutlery can last a long time if properly cared for (use if often, keep it sharp, use a wood or plastic cutting board and don't run it through the dishwasher). Henckel is the most popular brand of quality knives. Expect to pay $50-$100 for a good quality chef's knife. Shun seems to be highly regarded by professionals but expect to pay more. Since cutlery can be a lifetime investment it can be cheaper in the long run to get a good one rather than suffer through several cheap ones.
I don't know if they are the best, but we got a set of Farberware knives for our wedding and they seem to do pretty good. I have only had this set for about 2 months, but my friend has a very similar set of Farberware knives for a little over a year and he loves them.
If you just want a good day-to-day quality set, I got a set of ginsu knives, and a knife block, for $20 thru New Egg (http://funadvice.com/r/168754tq8a0. Hope this helps. Good Luck!!