Telescope marketing on budget models often leads with an impressively large magnification number, which is close to the opposite of what actually matters for a good telescope.
Aperture — not magnification — determines what's actually visible
Aperture (the diameter of the telescope's main lens or mirror) determines how much light the telescope gathers, which is the real limiting factor for how much detail and how many faint objects can actually be seen — a larger aperture reveals dimmer, more distant objects and finer detail, regardless of magnification. Magnification, by contrast, is a relatively simple math function of the telescope's focal length and the eyepiece used, and can be pushed arbitrarily high on paper — but magnifying a dim, low-detail image just produces a bigger, dimmer, blurrier image, not a genuinely clearer one. A telescope advertised with "650x magnification" and a small aperture is a strong warning sign of a low-quality instrument marketed around a number that doesn't reflect real usable performance, since that aperture can't actually gather enough light to make an image usable at anywhere near that magnification.
Refractor, reflector, and compound telescopes have real tradeoffs
Refractor telescopes use lenses, producing sharp, high-contrast images with low maintenance, but larger apertures become expensive and heavy, since a large, high-quality lens is costly to produce. Reflector telescopes use mirrors, offering considerably more aperture per dollar than a refractor of similar price, making them a common recommendation for beginners wanting real light-gathering capability on a budget — but they need occasional mirror alignment (collimation) and are generally bulkier. Compound (catadioptric) telescopes combine lenses and mirrors, offering a more compact design for a given aperture, at a higher price point than an equivalent reflector.
A sturdy mount matters as much as the optics
A telescope mounted on a flimsy, unstable tripod or mount will shake and vibrate with the slightest touch or even wind, making it genuinely difficult to get a clear, steady view regardless of optical quality — this is a common way an otherwise capable telescope becomes frustrating to use in practice. Checking mount stability and build quality, not just optical specs, matters for real usability, especially at higher magnifications where small vibrations become much more noticeable and disruptive.
Portability affects how often a telescope actually gets used
A large, heavy telescope with excellent optics that's cumbersome to set up and move outside tends to get used less often in practice than a smaller, easier-to-manage telescope that's actually convenient enough to bring out regularly. Being realistic about how much effort will actually go into transporting and setting up a telescope for a given observing session is worth factoring into the size and type chosen, not just maximizing aperture for its own sake.
The one thing people forget
Let a telescope acclimate to outdoor temperature for a period (often 20-30 minutes or more, depending on the size and how different indoor and outdoor temperatures are) before expecting sharp images, particularly for telescopes with larger mirrors. Temperature differences between the optics and the surrounding air create air currents inside the telescope that blur the image until the equipment reaches thermal equilibrium with the outside air — a real optical effect, not a sign of a defective telescope.