My knife recommendation is an 8 inch Chef’s knife
The frugal student’s kitchen is all about buying inexpensive, in-season products and preparing them at home. To accomplish this, my knife recommendation is a full-tang, 8 inch, non-serrated Chef’s knife. Let me tell you a little about why each of these is critical. Then you will avoid buying something that will be useless in a year.
If I’m going to recommend a knife, it must have a full tang. The tang is metal part that extends into the handle. Bad knives only have an inch or so of the blade that extends back into the plastic handle. The connection between the handle and the blade wears out, and the blade detaches. End of knife. A good knife has a full tang. An unsharpened extension of the blade goes all the way back through the handle.
8 inch length:
An 8 inch blade is a nice medium length. It is long enough to chop a good portion of vegetables, but short enough that you can peel an apple if you want. An inch shorter is probably fine, but not much more than that. With a little practice, there is really no need for a set of knives of various length. I don’t recommend a knife set. It is more to clean, more to move, and detracts more than it adds. I might add a paring knife (~3 inches) as it is nice for peeling and fine cuts, but I do fine without one. My knife recommendation is one knife: a Chef’s knife.
Serrated blades may seem sharper, longer, but it is not worth it. They are like saws and they do not make nice cuts. More importantly, once they are dull, they are thrown away. There is no good way to sharpen it. Serrated knives are, basically, disposable.
With a non-serrated knife, you just need to sharpen it every month or so. There are two kinds of sharpener: a “steel” and a “whetstone.” A steel looks like a knife with a round blade. It straightens out the edge of a blade that is just a little dull. A stone is an abrasive, like sandpaper. You can get one at most dollar stores. It is used to remove a little bit of metal to get a narrow, slanted edge. In principle, you can only use a stone so many times before your knife is not sharpenable. In practice, that number is so high that the knife will be in your family for generations. I prefer a whetstone. There are some great knife sharpening tutorials out there (here, here and here).
The shape of the knife is important, too. The Chef’s knife has the perfect shape. It is wide near the handle this allows it to chop without banging your fingers. It is still long enough and narrow enough to do most carving tasks. Longer Chefs knives have more leverage and can chop bigger, harder food. Heavier knives make this easier also, but can wear out the chef. I like an 8-inch and I don’t prefer a very thick, heavy blade. Plan on spending $20 – $40. I don’t recommend splurging more than that; there are beautiful knives that cost hundreds of dollars, but for most people it will not be very noticeable.