What are you shooting?
Your camera likely came with a so-called kit lens, probably a zoom in the 24-70mm (35mm equivalent) range. However, most kit lenses are useless in low light and have mediocre image and build quality. So you should strongly consider supplementing it with at least one or two additional lenses.
What to buy depends largely on what you think you'll be shooting. For most photographers, a versatile, wide focal-range zoom will be your best bet. Portrait photographers will want a 50-85mm fixed (prime) lens that best flatters the human face.
Product photographers might consider a macro lens, architectural and landscape photographers need wide-angle zoom or fixed lenses, and wildlife and sports shooters will be drawn to large, relatively fast telephoto (tele) fixed or zoom lenses. If you shoot a lot in low light, you'll need a fast lens (f/2.8 or lower) with stabilization, and video shooters will need to consider things like focus breathing, manual focus and parfocal qualities (more on those shortly).
Focal length and angle of view. The key feature of a lens is its focal length in millimeters. (Angle of view is much the same but takes into account the sensor size.) We often express focal length as a 35mm film camera equivalent so we can understand the relative angle of view for any camera. By that metric, lenses under 24mm are ultra-wide angle (or fish-eye, if there's significant distortion), wide are between 24-35mm, standard are 35mm to 70mm and telephoto lenses come in above that. Macro lenses, which capture very close subjects, are usually in the 35-100mm range.
Prime vs. zoom. Zooms are more versatile and make it easier to frame your subjects without moving while primes generally offer better optics and low-light performance (speed) for the same price. That's because there are optical compromises in zoom lenses that don't exist with primes.
Mount. Lenses are usually designed for specific brands (Nikon, Sony) and sensor sizes (full-frame, APS-C or Micro Four Thirds). Generally, lenses are a lot more expensive for full-frame cameras, because there's more glass. Full-frame lenses for Canon, Sony and Nikon work just fine on their APS-C models. You can also stick APS-C lenses on full-frame Nikon and Sony cameras, but the image will be cropped and zoomed in. Generally, it's best to buy lenses made specifically for your camera.
F-stop or aperture. Faster lenses with wider apertures (openings) have lower f-stop numbers, (f/2.8 instead of f/4.0, for instance), indicating that they take in more light. They also let you create more bokeh, or blur, in the background to isolate the subject. As a rule, they cost a lot more than slower models. Cheaper kit lenses often have variable apertures, which change depending on the zoom level. For instance, Sony's slowish full-frame FE 28-70mm OSS kit lens has a variable f-stop range of f/3.5-f/5.6 and costs just $398, the Vario-Tessar T* FE 24-70mm f/4 ZA OSS model is $898, and the fixed-aperture FE 24-70mm f/2.8 GM lens will set you back $2,198.
Autofocus (AF). If you buy an extremely fast camera like Sony's A9, you'll want a lens that focuses just as quickly. Again, money helps here, as costly Canon RF models, Fujinon, Nikon Z and Sony GM glass mostly offer great AF performance. That said, many cheap kit and prime lenses, like Nikon's 35mm f/1.8 Z-mount, also pack solid autofocus systems. Cheaper lenses can have noisy autofocus, which is something that video shooters, especially vloggers who rely on AF, should keep in mind.
Stabilization. Stabilization reduces hand and other camera movements (though not subject movement, obviously), letting you shoot with less light than you normally could. If you have certain mirrorless cameras like Nikon's EOS R or Sony's A7 III, they already have built-in stabilization (IBS). For other models, though, you'll need to get that feature from the lens. The key metric is how much extra speed you get (in f-stops) compared to having no stabilization. Many lens makers claim as much as three to four stops of improvement, but keep in mind that it won't help on every shot. Note that even if your camera has IBS, you'll still benefit from a lens that has it, as most IBS systems work in concert.
Optical quality, bokeh and distortion. Generally, most modern lenses, including kit models, are sharp enough for the average user. Better lenses, however, will remain sharp at wide-open apertures and toward the corners of the image with less vignetting, or dark corners.
Higher-end models will also have better, softer-looking bokeh in the blurred parts of the image. As for distortion, it's mostly an issue with zoom lenses, not primes, and modern mirrorless cameras will automatically remove it. Zoom lenses, especially cheaper models, are also more susceptible to chromatic aberration (CA) that causes blue or pink tones at the edges of objects in a photo.
Handling, manual focus and other factors. Expensive zoom and prime lenses can be heavy, cramping your style for street or tourist photography. If you want to travel light, then, a pancake, light prime or a lightweight kit lens will do the job best.
Though most photographers don't need manual focus, it's still important for videographers who rack (change focus) from one subject to another. Video pros will also want a lens with a lot of focus-ring travel for finer control and models that don't breathe, or zoom, when you change focus. (Purpose-built cinematography lenses don't breathe but are expensive.) For zooms, videographers might need parfocal lenses that stay in focus when zooming -- again, these tend to be costly.
Best budget standard prime lenses
If you already have a kit zoom lens with your camera, the next step is to get at least one prime. Why? It will let you shoot sharp, distortion-free portraits or take street and travel shots with nice bokeh. You'll also be able to shoot in bars, concerts and other low-light situations without cranking up the ISO and creating noisy images.
Luckily, this is fairly easy: Every brand has a cheap, fast, "nifty fifty" prime that will take surprisingly nice shots. Sure, they're plasticky and not as durable as higher-priced primes, but they're also lighter, and thanks to modern manufacturing techniques, the optics are great.