The best telescope under $300 is a tabletop Dobsonian, not a refractor on a tripod. Aperture is the spec that actually determines what you will see, and a 130mm Dobsonian gathers more light than any refractor at this price. Every all-in-one kit at a big-box store advertises the same three lies: a magnification number in the hundreds, a paper-thin tripod, and a lens cap sturdier than the optical tube. None of that matters. Three specs decide whether a budget telescope is worth owning: aperture, useful magnification, and mount stability.
Aperture is the diameter of a telescope's main lens or mirror, measured in millimeters, and it is the single spec that determines how much you will actually see. Light-gathering power scales with the square of aperture, not the diameter itself, so a 130mm mirror collects roughly three and a half times the light of a 70mm lens, not just twice as much. Bigger aperture also resolves finer detail and reveals fainter deep-sky objects: star clusters, galaxies, nebulae. Magnification is a function you control with eyepieces; aperture is fixed the day you buy the scope. Buy the aperture, not the box art.
Magnification is aperture-dependent too, just not the way the box claims. The rule amateur astronomers actually use: useful magnification tops out at roughly 1.5 to 2 times the aperture in millimeters. A 130mm scope has a realistic ceiling around 195x to 260x, on a very good night, with steady air and good optics. Push past that and you are just magnifying blur: atmospheric turbulence and the mount's own wobble degrade the image faster than more magnification can reveal detail. A 130mm Dobsonian at 150x, in focus, on a still night, shows more of Saturn's rings than the same scope wobbling at 675x ever will.
Focal ratio is the focal length divided by the aperture: a scope with a 650mm focal length and 130mm aperture is f/5. Lower focal ratios, f/4 to f/6, give wider fields of view and forgiving eyepiece requirements, exactly what a beginner wants for sweeping the Milky Way or hunting star clusters. Higher focal ratios, f/10 and up, suit close-up planetary and lunar viewing but need pricier eyepieces to feel comfortable. None of that matters if the mount shakes. A tabletop Dobsonian's low center of gravity and simple rocker-box design make it inherently more stable than an aluminum tripod at the same price, which is the real reason experienced buyers point beginners toward Dobsonians first.