1) 8 x 45 or 10x50 Binoculars are the cheapest option for anyone with a casual interest, and especially for parents with children for whom astronomy may be just a passing fad. However, if you can't hold them steady enough you will never get any satisfactory views wiithout the additional expense of a tripod or mirror mount. Or, if you can afford it, consider the Canon 10x30 imaged stabilised binoculars at around £330 for rock steady viewing. They are good for learning your way around the sky and absolutely brilliant for wildlife and other activities.
2) Magnification isn't that important, Aperture is! There are, unfortunately, a lot of cheap telescopes marketed with totally unrealistic claims such an 877 magnification for a 127mm (5 inch) scope. The maximum magnification for any scope is usually around 50 x the ins aperature or 2x the mm. But most nights you will probably be limited to half that. Lower magnification often equals a sharper view and is usually better for the fainter objects like nebulae, whilst planets like Jupiter and Saturn can take higher magnification.
3) Where to buy. To see the Moon, planets and the brighter objects any telescope bought from a reputable company (more about that later) will enable you to do just that.
4) Size and Cost. The bigger the scope (mirror or lens) the more you will see - and the more it will cost. A 6in (150mm) scope will start to show many of the more interesting faint fuzzies, but unless you have dark skies you will need at least an 8in(200mm) scope to show any real detail. However, viewing conditions in the UK are such that although the bigger scopes show more, you will get far better, steadier views through a smaller scope and be able to use it far more often than with a large one. And don't expect to see the colour that you get in astro-images.
5) Relative Costs. Reflectors of the same size and similar specification will always be cheaper than Refractors, and Catadioptrics will be more expensive than all except the high end Refractors. And GOTO scopes are more expensive than manual ones.
6) Manual v Motorised v Computerised. A manual scope will always be cheaper than a motorised or computerised scope, but you will constantly have to move the scope to track the stars and planets. And where light pollution is a factor you will find it difficult to locate anything other than those objects visible to the naked eye. A motorised scope will enable you to track an object without having to constantly move the tube. Once you have done the initial alignment a computerised GOTO scope will find objects for you.
7) Equatorial mounts take a bit of time to get used to and the eyepieces of Reflectors and Refractors can end up in awkward positions compared with Catadioptrics.
8) Images. Refractors give the sharpest images but the cheaper ones may suffer from colour fringing.
9) Magnification. A short focal length telescope will give a lower magnification and a wider field of view than a long focus one for any given eyepiece. High magnification is not necessarily a good thing as if the viewing is poor all you get are wobbly, distorted images whereas a lower magnification will give you a much clearer, sharper image.
10) Light Pollution. For many objects other than the Moon, planets and those visible to the naked eye, Light pollution will limit what you can see with the smaller scopes. And at Full Moon often the only thing you can see clearly is the Moon!
11) Finderscopes. Red dot finders are only good for finding objects that you can see with the naked eye. Finderscopes - small telescopes - make life much easier as they make more objects visible and have a wide field of view.
12) AstroPhotography. If you are sure that AstroPhotography is likely to be your main interest then ideally you should go for a short focal ratio scopes (around 5) and an Equatorial Mount. However, good results can still be achieved with longer focal ratios and Alt-AZ mounts, especially when imaging the Moon and the Planets.
For much of the UK where there is at least a moderate level of light pollution
Computerised GOTO scopes make it much, much easier to find objects, especially for beginners
alternatively a manual scope with a minimum aperture of 130mm is recommended
see comments under suppliers.