What can I see with a microscope at what magnifications?
You'll be able to see something that is 1 micrometer as a slightly formed (meaning you can decide whether it's more oblong ore more round) dot. So any structure that is bigger than that can be better observed. Unfortunately, viruses are far smaller, and many interesting cel organelles are too. 



Also, many things (like parts of cells) are not visible until they are stained. There are many stains that are suitable for beginners (others are quite toxic or teratogenic). I'd recommend buying a book from 1970 or before (no re-issue), because many stains and chemicals are nowadays deemed too dangerous (although they are not that dangerous if used in amateur-microscopy volumes) and normal light microscopy technique has not changed since then.

With a used microscope from a reputable manufacturer (inquire beforehand whether the tubes are of a standard size so you can get replacement oculars etc.) you are on a good way. Schools and universities will sometimes purge their stock, which is where you can make incredible deals.

Get a microscope with mains-fed light, ideally LED. Some 'tricks' like Dunkelfeld are very interesting to use, but require a good light source and non-broken iris.

Also look at the table, it should have a smooth, no-hysteresis (meaning if you go left, and then right, there should be no 'slack' to take up before the picture moves the other way) x/y platform, ideally with a measure attached.

Total magnification is ocular*objective, and many microscopes offer the possibility to attach a camera, either additionally or as replacement ocular. that is a great thing, as you can take pictures and zoom in (real magnification will not change, but still, some things are easier to see that way) or later tweak the colors or contrast.

Depending on whether you mainly want to look at things that can be put between two glass slides (cells, bacteria, small parts of insects, ...) or at 3D things (insects, flowers, minerals) you can either buy a two-ocular microscope or binocular (3D) or a one-ocular microscope. 

Objectives and oculars are small tubes with many lenses built into them - this means humidity and even rot can slip between those, so be sure to check used material (especially from learning institutions) for clear pictures.