This is a topic that could have many different opinions. The decision is normally what gauge strings to use. I am going to discuss the basic differences and effects of the different gauges.
It is often said that a guitar is made for a certain gauge string and if you change the gauge, from say a medium gauge to a light gauge, changes take place, like your action gets higher - this is to a certain extent true. The action will change, here is the reason:
In guitar making, when a guitar is made and finished, it is set up for the gauge strings that are put on at the time of set up. There are predominantly three gauges; light, medium and heavy (you can for example, get variations like medium light). With a light gauge, the strings are thinner and you do not have to put as much tension on the string to tune it, hence, it bends, or frets easier, you do not have to push as hard, making it easier to play. I you go to the extreme and put a heavy gauge on, you have to put more tension on the string to get it to tune, now when you play, you have to push much harder to fret the string. With the heavier gauge string and the increased tension, there is now more stress on the neck, in other words, because of the increased tension, the heavier strings will cause the neck to bend more toward the body creating more of a bow and thus causing the action to be higher and probably affect the intonation. This does not mean that the guitar was not built for this and that it will cause damage. It means that the guitar was made well, it will need to be set up for that gauge of strings. On my course on guitar making, you learn how to set up a guitar and then will be able to adjust your guitar should you change the string gauge. If you are not sure how to do this send your guitar to a Luthier and ask him to do the change and adjust the set up.
Why then use different gauge strings?
The different gauges result in different sounds. A lighter gauge will be easier to play and will produce a brighter sound. A heavier gauge will require more tension, will be harder to play, and will have a more full sound. The medium gauge gives the best of both. The main thing to worry about is how hard you play the guitar. If you strum very hard, you will probably want heavier strings, and if you have a lighter touch, you will probably like lighter strings. . Bending strings requires more strength, the more it will cut into non-calloused finger with thicker strings, but the sound tends to be fuller and heavier. Light strings are easier to play leads with and can still give a guitarist a very strong sound.
To hear the difference that a thicker string won't sound as bright try this:- Play something on the high E and compare five frets up on the B string, then another four on the G string, and you'll hear that difference.
This is just one of the many interesting aspects that make a guitar the special instrument that it is.