First it depends what kind of photography you want to do. I'm going to talk about 6 basic categories of lenses which are useful for some types of photography but not so much others.
1. The (ultra)-wides: for wide vistas, architechtural exteriors and interiors - they are able to fit a great deal into the frame and for a special perspective- they make near objects big and distant objects very small. There are some nice examples here. Wide angle lenses like 35mm equivalent can be a good everyday lens especially for a photographer who likes to get in close1.and 2.
2. The standard lenses are so called because they capture a frame similar to what we normally see in terms of the angle (width). A typical kit zoom (24-70mm) includes the wide angle and the standard, as well as a mild telephoto. A standard prime is typically 50mm and they are generally very good! If you are not really interested in equipment, spend a few hundred $$ on a prime 50mm to see if you can discern any difference from your kit zoom. If not, then your mortgage is safe. Otherwise, you may embark on a great adventure that some unsympathetic souls have labelled LBA (Lens Buying Addiction).
3. True macro lenses is something you need if you like to shoot small critters very closely. They have a label 1:1 which means they reproduce the object up to life-size on the sensor. They also tend to be very sharp and good for other things too. With a macro you can focus very close whereas with most lenses you will occasionally find yourself unable to focus because you are too close to the object. Some lenses have a label macro when they are not true macros, but simply to say that you can focus closer than usual with them, perhaps even into the "macro" range like 1:3, which can be handy, but they are not 'true' macros.
4. Telephoto lenses are obviously for shooting things that are further away, but they can also be handy for blurring the background to isolate the subject as in a portrait. The more 'tele' the lens is, the more it will isolate the subject that is in focus, all other things being equal. Telephoto lenses do vary in quality a lot, they have different wide-open (lowest value) aperture (which limits how much light they are able to let in), different levels of correction for various aberrations, flare, some come with handy vibration reduction and of course sharpness and contrast. The big caveat is that the best ones are usually very large and heavy and this is going to matter in many practical applications.
5. Prime vs Zoom vs Super-zoom. Prime lenses generally tend to be better optically, but in terms of functionality, they tend to be faster, ie let more light in (allow lower value aperture), which makes it more feasible to shoot in dim light and to control how much of the frame would be in focus (depth of field). They are smaller and lighter usually and importantly they are easier to get used to - after a while you know what the frame will look like. But of course they are fixed focal length, which means you can't zoom. Zooms have gotten heaps better, even the kit zooms are often not bad, especially away from their boundaries at either the focal length or the aperture but superzooms, the ultimate in convenience, still has a long way to go. So if you've invested in a very good camera, such lenses are not going to take full advantage of that sensor - they will blur the image with their optics.
6. Specialty lenses. These include Perspective Correction or Tilt-shift lenses which are very good for architectural photos where you don't want your buildings tapering off and can also move the plane of focus to create weird effect and Lens Baby optics for all sorts of bizarre blurs and effects.
So if there is a style of photography you gravitate towards, get a lens that does the trick and as you begin to feel its limitations, upgrade.
Brands? Modern lenses are pretty damn good. Even cheap ones are reasonable. The law of diminishing returns kicks in big time with lenses. An $800 Sigma 35/1.4 to $5500 Leica Summilux 35/1.4 Asph FLE is going to make very little difference if you manage to stick both on the same camera that is. Of course the Leica is heaps smaller, fits a Leica body (yes, they do make digital camera) and looks the price. All major manufactures produce some very good lenses (and some that are quite average). Most of the difference will show up in the richness of the image - tonal range, colour fidelity, the 'pop' 3-d -like quality of the image that can make it very lifelike. But what people seldom hear is that much of the difference comes from postprocessing the image well - the work that happens on the computer after the shot has been taken. If you are wondering where to invest your money and time, then getting good photoprocessing software and learning it well, is probably a better investment than splurging out on the latest optical marvel.
Conclusion: It's a jungle out there as far as equipment goes! But the good news is that even the basic kit lens with a dSLR is already a powerful instrument and once you begin to feel its limitations, by all mean there are alternatives. But whenever you see a special look to a photo, chances are it is the light, the skill, the filter or most likely the post-processing more so than the lens. Lenses can and do make some difference as far as what kind of scenes you can capture and how rich your final image can be, of course, but rarely as much as the price of the best ones would seem to suggest.
If you're adventurous and want to see some great quality on little budget, get the little Sony NEX-5n ($280 used), a Metabones Contax G to Nex adapter ($120), and some of the Contax G lenses. The cheapest is probably 90/2.8 ($220) and is already excellent, but the most practical is 45/2 ($450). These are superb, small and easy to use on the 5n if you are not afraid of Manual Focus. Compare it to the Sony kit zoom and see what the fuss is about. A picture, as they say, is worth a thousand words.