Thank you Pyrroh for the great help! Getting slightly off topic, how do ohms work?
For practical purposes, there are several things worth knowing.
First, the impedance of a speaker tells you nothing about how it sounds. A low impedance speaker may sound great or terrible or anything in between, and a high impedance speaker may sound great or terrible or anything in between. However, there are quite a few great speakers that are fairly low impedance, and this is often the case because people who can afford them can afford to buy a good amplifier, so the designer need not worry too much about what impedance the speaker ends up being. A good designer of budget speakers will, however, be more constrained in choosing things, as it would be quite silly to design a budget speaker that is insensitive and 1 ohm nominally, as it would take a pretty expensive amplifier to be able to deal with it.
The impedance is an electrical characteristic of the speaker. Its importance lies in matching the speaker with an appropriate amplifier. In general, the lower the impedance, the greater the difficulty in driving it, but there are amplifiers designed to drive low impedance speakers with ease.
Impedance is opposition to alternating current (audio signals are alternating current). It is called "impedance" rather than "resistance" because it varies with frequency. Thus, a speaker may be 8 ohms at 1000 Hz and 6 ohms at 5000 Hz. A graph, called an impedance curve, can represent the impedance of a speaker at every relevant frequency (they don't typically measure the impedance at 500,000 Hz as that is irrelevant to audio gear). When a manufacturer gives a speaker a "nominal" impedance rating, it is supposed to be that, overall, one can consider the speaker that impedance. However, as I mentioned before, some speaker manufacturers are not good about this, as they like to put "8 ohms" on them so that people who have amplifiers that are rated for 8 ohms minimum will still buy them. So some manufacturers who have no scruples or morals will put that "nominal 8 ohms" label on a speaker that has a dip in the impedance curve of, say, 4 ohms at 80 Hz. That is not good, because the demands on the amplifier will be greater than the unwary buyer is likely to realize. And that is why it is good to find the minimum impedance. With a nominal 8 ohm speaker, typically it will be okay if the minimum impedance is one or two ohms lower, but it should not be dramatically lower, if one is going to use it with an amplifier rated for 8 ohms minimum. Really good companies are careful about such things. (I don't know what their current policy is, but McIntosh used to have a policy that their nominal impedance ratings for their speakers would be such that they never had a minimum impedance lower than 10% less than the nominal rating, or in other words, no lower than 7.2 ohms for a nominally 8 ohm speaker. That is the sort of policy that a good company will have, but evil lying bastards abound in business, so you should try to find a professional review in which they measured the speaker to find out the minimum impedance of whatever speaker you are considering [some manufacturers also state the minimum impedance of a speaker, and then you need not find a review for this information]. And pay attention to which companies are liars about this sort of thing for future use, in case you can't find a review of the particular model in question, to have some idea of which companies are not generally trustworthy.)
Back to the first point I made, the very best sounding speakers that I have ever owned (which also have the most expensive retail price of any speaker I have ever owned) are 3 ohms nominally (with no dramatically low dips in the impedance curve; an honest company, at least about this model), which require a good quality amplifier to drive them. I use them in my main 2 channel system. But the second best sounding speakers that I have ever owned are 8 ohms nominally (with no dramatically low dips in the impedance curve; another honest company, at least about this model), and I use them in my home theater.
When auditioning speakers, you can ignore the impedance issue. But when you finally select whatever speakers you think sound best in your price range, then you need to research the impedance of them to find out what sort of amplification you need. The louder you like your music, the more it will matter, and the more insensitive the speaker, the more it will matter. If you never push things hard, you can probably just "trust" the nominal ratings of impedance and be done with it, but if you do like to play things loud, you had better make sure there are no nasty dips in the impedance curve that your amplifier will struggle with. Either that, or you need to just spend a fortune on a great amplifier that can deal with any speaker ever made, but that is not a very cost effective approach, and would not work well with your budget (or most other budgets).
So, audition speakers without concerning yourself with such things, and then after deciding which speakers you like best, do the relevant research. With listening to speakers, you may very well like two or three models of speakers more or less equally, in which case you may want to research all of them, in case one of them is really out of your price range due to impedance issues that will require a greater investment in amplification.
If you are lucky, you will end up liking speakers that are very sensitive (i.e., will output high volume with low power) and are an honest 8 ohms nominally (which will be compatible with pretty much every amplifier ever made). But unless you listen at volumes loud enough to permanently damage your hearing, or have a huge room (like an auditorium), this is not going to be necessary, and a speaker of ordinary sensitivity will be fine with pretty much any decent receiver you can buy.