The speakers are the most obvious component of a monitoring environment, but not necessarily the most important. It’s also not simple to choose speakers.
Full-range monitors usually have large woofers and are designed to produce sound down to low frequencies (in addition to high frequencies). These monitors try to reproduce the broadest range of sounds. Because of this, these can be attractive as “first” monitors. Be aware though, that there’s no free lunch. Reproducing those lower frequencies requires large cones, which are good at reproducing lower frequencies but aren’t so accurate at higher frequencies. The top of the frequency range is usually covered by the tweater, which is good at reproducing high frequencies but not as strong on lower frequencies. This approach results in a speaker that is strongest at high and low frequencies but might be weaker in the mid-range.
Another approach to the size/frequency trade-off is to use a medium-sized woofer with a tweater. This approach focusses the strength and accuracy of the speaker in the middle and high frequencies. This is good for making a lot of mix decisions, because the mids and highs is where the most instruments are playing together and where its most important to get the balance right in the mix. The drawback, of course, is that these speakers are weakest in the bass. This can be a particular problem when working on modern electronic music, where the kick and bassline are extremely important.
A common solution to the problem of smaller speakers’ bass response is to add a subwoofer. This is a third speaker focussed on the lowest frequencies. This has the potential for a more accurate approach across the whole frequency range. The drawback, however, is that it’s easy to mis-configure the subwoofer (usually by making it too loud). The way the subwoofer works with the other speakers depends greatly on the room their placed in, meaning the configuration is very much up to you (or whoever configures your room for you). It’s common to hear large amounts of bass as pleasing or exciting, making it difficult to resist the urge to configure the system to sound exciting instead of accurate. Another problem more common with cheaper subwoofer-based systems is that the front speakers are too small to reproduce the lower mids (which are poorly compensated for by the subwoofer) , and the subwoofer is too small to accurately reproduce the lowest frequencies anyway.
Of course, a well-rounded monitoring environment consists of more than one set of speakers so that the weaknesses in a single set doesn’t become a weakness in the whole monitoring environment.