I plan on buying a cheap amp, but most of the ones I see have a impedance of 4 ohms where my speakers have a impedance of 8 ohms, would it hurt to use 8 ohms on a 4 ohms amps. Also what does it mean when an amp has an impedance of 4-8 ohms or 4-16 ohms.
Generally amps will not drive low impedances - less than 2 ohms. There are very high quality amps that can do this but cost $$$. An amplifier rated for 4 - 16 ohm impedances will drive anything 4 ohm and above. The only thing about amplifiers and loads is to get maximum power transfer the load and amplifier should be matched. An amplifier with a 4 ohm impedance will transfer the greatest amount of power into a 4 ohm speaker.
The amp does not have an 8 ohm or 4 ohm impedance. If has a power rating when used with speakers of those ratings. If you have 8 ohm speakers those will play with any amplifier you can find. Some amps however give their power rating into 4 ohms (makes it look bigger) so you will have to cut that figure in half when used with an 8 ohm speaker.
^ It also means they can drive 2 sets of 8 ohm speakers in parallel - cheap amps will put A & B speakers in series so that they can drive them - 16 ohm load each receiving 1/2 the power per side. Some amplifiers will give their ratings at 2 or 4 ohms - yes the numbers will be bigger but more important is they can actually drive these low impedances. Amplifiers and their specs are meant to dazzle/baffle the average consumer - best specs do not always make the best amplifiers.