The most common mistake people make buying a first telescope is reading the box. Telescope boxes in department stores and big box retailers are covered in magnification numbers. 300x. 400x. 500x. These numbers are essentially meaningless for anything you would actually want to look at, and the telescopes that advertise them are almost uniformly disappointing to use.
The second most common mistake is spending too little and getting something that makes the experience worse than using no telescope at all. There is a floor below which a telescope does more harm than good, and it is roughly $200. Below that, the optics are usually poor, the mount is usually unstable, and the experience of trying to find and track an object is frustrating enough to put people off the hobby entirely.
Here is what actually matters, and what to buy.
Aperture is the only number that matters
Aperture is the diameter of the main lens or mirror, measured in millimeters or inches. It determines how much light the telescope collects, which determines how faint an object you can see and how much detail you can resolve. More aperture means more of the universe is accessible to you.
Magnification is what you get by combining the telescope's aperture with a specific eyepiece. Any telescope can produce any magnification if you put the right eyepiece in it. But magnification beyond what the aperture can support just produces a larger, blurrier image. There is a practical upper limit for any telescope, and it is usually far below the numbers printed on the box.
A 6-inch aperture telescope at 100x will show you more than a cheap 3-inch telescope at 400x, every time, in every condition.
The mount matters as much as the optic
A telescope on an unstable or poorly designed mount is almost unusable. Every vibration from touching the tube ripples through the view. Every attempt to track an object across the sky becomes a fight. The mount is half the instrument and is treated as an afterthought in the budget end of the market.
There are two basic mount types worth knowing. An alt-azimuth mount moves up-down and left-right, which is intuitive but requires two simultaneous adjustments to track an object. An equatorial mount is aligned with the Earth's rotation axis and can track objects with a single smooth motion, which is useful for higher magnification viewing and astrophotography. For a first telescope, alt-azimuth is usually fine.
The Dobsonian mount is a specific type of alt-azimuth that is simple, stable, and allows very large apertures at low cost. It is the reason the Dobsonian design dominates the recommendation lists of serious amateur astronomers for beginners.
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What to actually buy
For someone spending $200 to $350, the Sky-Watcher 6-inch Dobsonian is the most recommended first telescope in amateur astronomy communities for good reason. Six inches of aperture on a stable rocker box mount, simple enough to set up and use on the first night, dark enough skies required to show you things that will genuinely surprise you. The views of the moon, Saturn's rings, Jupiter's cloud bands, and the Orion Nebula at this aperture are immediately impressive. It is not a beginner telescope in the condescending sense. It is a serious instrument that happens to be approachable.
For someone with $350 to $500, the Sky-Watcher 8-inch Dobsonian is the better version of the same idea. Two more inches of aperture makes a real difference in how many objects are accessible and how much detail is visible. If you are confident you are going to use it regularly, the 8-inch is worth the extra money.
For someone who specifically wants a computerized telescope that finds objects automatically, the Celestron StarSense Explorer is worth considering in the $300 to $400 range. It uses your smartphone's camera to identify star patterns and calculate where the telescope is pointing, then guides you to any object in its database. The tradeoff is that you learn less about the sky by navigating to objects manually. For someone whose primary goal is just to see things rather than learn the sky, it is a reasonable choice.
For someone who wants the most portable option, a 70mm refractor on a lightweight alt-azimuth mount in the $150 to $200 range gives acceptable views of the moon and bright planets and is easy enough to carry anywhere. It will not show you faint deep sky objects but it will work and it will not frustrate you, which is more than can be said for anything cheaper.
What you can realistically expect to see
A 6-inch telescope under a Bortle 3 sky on a steady night will show you craters on the moon in extraordinary detail, the rings of Saturn with the Cassini Division visible as a gap between the rings, the cloud bands of Jupiter and its four large moons, the Orion Nebula as a cloud of glowing gas rather than a smudge, and dozens of star clusters sharp and clear against the dark background.
It will not show you the colorful nebula images from the Hubble Space Telescope. Those images are long-exposure photographs that stack hours of light collection. The human eye through an eyepiece sees in real time with no accumulation. What you will see is detailed, subtle, and occasionally breathtaking, but it requires a shift in expectations from the photography you have seen online.
The moon, paradoxically, is the worst target for dark sky purposes. It is so bright it washes out everything else around it. Serious observers plan their dark sky trips around the new moon specifically to avoid it.
One thing to buy alongside the telescope
A red-light headlamp. Your eyes need 20 to 30 minutes to fully adapt to darkness, and a single white light from a phone screen resets that process entirely. A red-light headlamp lets you read star charts, adjust the telescope, and move around without destroying your night vision. Every observing session should start with red light only and stay that way until you are done. It is a $15 to $25 purchase that changes the quality of every night out.
The honest version
A good pair of 10x50 binoculars will show you more of the sky in a more accessible way than any beginner telescope under $200. If you are not sure you want to commit to a telescope yet, start with binoculars. They are easier to use, more portable, give wider fields of view, and work well for the moon, star clusters, and bright nebulae. If after six months of binocular use you are still going out regularly and wanting more detail and magnification, you will know exactly what kind of telescope to buy and you will use it.
If you are confident you want a telescope, buy the biggest Dobsonian your budget allows and learn the sky manually before adding any electronics. The night you find Saturn for the first time by star-hopping from a known reference point is more satisfying than the night a computer points you at it automatically. Both work. One teaches you something the other does not.