You've been taking pictures on your point-and-shoot camera and your cell phone for years, and it's been all well and good, but you want more. You know there's a whole world of photographic choices and possibilities that pocket cameras and multipurpose devices can't match. So you pick up a digital SLR and get ready to dive into the world of serious photography.  
 
Now you have to deal with the lens question. If you're buying an entry-level digital SLR like a Canon Rebel T2i or a Nikon D5000, then you're probably getting a "kit" consisting of the camera body and an 18-55mm, f/3.5-5.6 lens. While it'll certainly let you take pictures and your results will look better than anything you've done with a point-and-shoot, that kit lens is inferior to almost any after-market lens you could pick up. If you're serious about getting into photography, you'll want to pick up at least one decent lens on top of your new SLR kit. Of course, before you make a decision, make sure you go with the right lens brand. Canon lenses work with Canon bodies and Nikon lenses work with Nikon bodies. You can't mix and match. 

We'll teach you the technical attributes of lenses and how to pick a great one to use while you learn the ins and outs of your new camera.
 

Know Your Lenses

Before you look at lenses, it's important to understand the basic characteristics of lenses and be aware of why exactly your kit lens is an inferior product. Camera lenses have two general attributes: f-stop and focal length. The focal length is the most prominent aspect of a lens, because it dictates exactly how far you can zoom in or how wide you can pull back. The larger the number (measured in millimeters), the higher the magnification. An 18mm lens can take a very wide photo, while a 250mm lens can get very close to far-off subjects. However, that's only half of the equation. The other half is the lens's f-stop, and it's just as important. 
 
The f-stop, otherwise known as the aperture, determines your depth of field (the area in focus) and how much light can pass through the lens to reach the sensor. The rule is that the smaller the number, the wider the aperture and the more light that can hit the sensor. This is extremely important, because it determines how fast and at what light sensitivity (ISO) your camera can shoot in different lighting conditions. The difference between an f/1.8 lens and an f/5.6 lens can be the difference between a clean picture of a church at dusk shot at ISO 400 or a grainy image shot at ISO 3200. The width the aperture also determines how narrow the focal plane is; a wide aperture will let you focus sharply on your subject while leaving the background out of focus, while a narrow aperture will make everything in both foreground and background look sharp. 

Lenses can vary their apertures, and the f-stop number listed when shopping for a lens describes the widest possible opening; an f/1.8 lens can open up to f/1.8, but can also close down to f/2, f/4, f/8, and so on. For lenses that can vary their focal length, the f-stop range matches the range of the focal length; the 18-55mm, f/3.5-5.6 kit lens can open up to f/3.5 at 18mm and f/5.6 at 55mm. As you move onto the more expensive zoom lenses, they maintain a constant aperture. These lenses, like the 24-70mm f/2.8, are the favorites of professional photographers.
 

Start with the budget basics

Chris Gampat of The Phoblographer knows his lenses, and brings up a handful of options for replacing the mediocre kit lens that came with your SLR. There are many, many different lenses available, but Gampat recommends that first-time DSLR owners start off with a simple 50mm prime lens. Canon and Nikon offer 50mm, f/1.8 lenses for $99 and $125 respectively, and they can get you started shooting sharp, vivid images on a shoestring budget. If you can afford to spend $300 to $350, you can pick up an f/1.4 lens that's even sharper and brighter, but for the moment it's best to take baby steps and ease into the photography game.  
 

A Lens for getting personal

If you want to move a little bit closer with your pictures, we suggest an 85mm lens. In fact, according to Gampat, an 85mm lens is a vital part of anyone's camera bag. It provides the ideal amount of magnification to frame portraits, and let you get great detail at concerts, weddings, and other events without moving up so close you disrupt the proceedings. It's more expensive than a 50mm lens at the same f-stop, though; 85mm f/1.8 lenses for both Canon and Nikon SLRs can be found for $300 to $350 on this budget lens round-up. 

Taking the broad view

For a slightly wider view than a 50mm prime, a 35mm lens offers more flexibility when shooting landscapes and vistas. While it won't get as wide a shot as an 18-55mm kit they're much brighter lenses. Canon's 35mm f/2.0 lens is available for $330, while Nikon's 35mm f/1.8 can be picked up for just $200. Of course, the lens depends on the camera; if you have a Canon SLR, don't think you can save $130 by grabbing the Nikon. Without the right body, the lens is useless. 
 

Zoom zoom

Finally, if you want sheer telephoto flexibility at the expense of f-stop numbers, you can pick up a 50-250mm, f/4.0-5.6 lens for $300 or less. On one hand, you'd be able to get much closer than the 85mm lens, and you'd still be able to pull back to 50mm. On the other hand, at f/4.0-5.6, the lens is darker and less sharp than a similarly priced prime lens. Large, variable-zoom lenses also tend to be much heavier than prime lenses, which is another thing to consider. Gampat notes that some variable-zoom lenses can be useful, but cheaper ones (like ones available for $300 or less) offer inferior image quality and says that if you value sharp photos on a budget, you should stick with a decent prime lens or two. In contrast, a very good variable-zoom lens like Canon's 24-105mm f/4 lens costs over $1,000.  
 
The best thing you can to do get started with a decent lens is to grab a $100, 50mm f/1.8 lens. It's flexible and will offer sharp pictures that your kit lens won't come close to. Once you're comfortable with that, consider picking up a quality 35mm or 85mm lens. While more expensive, they're even more useful in certain roles and still offer excellent image quality for a good price. If you really want a powerful telephoto lens, you'll have to decide whether you'll be satisfied with an inferior picture or if you're willing to sink a lot of cash into getting a long zoom. For most photography, however, you'll have the best time between 35mm and 85mm. 
 
What was the first lens you bought for your DSLR?
 
Image credits: Flickr users Sweetsop (lead image), Velo Steve, Lord colus, Julio Aguiar, 96dpi, Robert Donovan, Filan, Steve Keys