Your child has decided they like space. You can start for free, and leave the telescope until you are sure one is right.
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☕ Buy us a coffeeThe single best thing you can do is go out on a clear night and look at the Moon. Look at it first with your eyes alone, then through any binoculars you have, and notice that the line between light and dark is rough. Those are mountains and craters, casting shadows. A child who has noticed that themselves has a different relationship with astronomy from one who has been shown a photograph.
Most pictures your child has seen of a nebula took hours of exposure, many of them on telescopes far bigger than anything you can buy. Through a small telescope, the same object is a pale grey smudge. What to buy, in what order, and why the cheap mount is the part that ruins it, is a longer answer with a page to itself.
That smudge is why the eyepiece views here are drawn to match what a small telescope really shows, not photographed. Not everything disappoints, though: a first look at Saturn is a surprise, not a letdown. The rings look painted on.
A telescope moves the hobby up a level, and the first thing it teaches is how much work it is. Finding one faint object can take a whole evening. Most evenings are clouded out. And when you do find it, you often cannot be certain that the smudge in the eyepiece is the thing you were looking for rather than the thing next to it.
None of that is the telescope failing. Work that takes a long time, produces a result you are not sure of, and has to be checked against what other people found — if there is a better definition of science than that, it is hard to think of one. A child who has stood in the cold and not found the galaxy has been taught something no lesson can teach them.
For the cloudy nights:
People worked it out from the ground, one step at a time, starting with a stick in the sand. There is a page for each step, and each one ends in something you can try together.