Much has been said already about string selection and if you're new then you've probably made up you're mind. If you do feel like experimenting though here are a few more things to keep in mind.
Different keys
A key centre basically determines how high or low the song is. You may want to play a song that was originally in E major and bringing it up to G just makes it too hard to sing. You may still be able to play a song in E when you're tuned to G, depends on the song, and your skills, and your guitar and probably a few other things as well. For the sake of our exercise here let's say you want to retune your guitar.
151 in E is EBE, on a 4 string 1513 is EBEG#. From G you just need to tune everything down 3 steps. This will reduce the tension on the strings so your guitar won't snap in two, if your strings are too light though you may lose too much tension making slide and vibrato very difficult. The only way to really tell is to try it but at least now you know what is going on.
Say you want to go up to Bb, that's 3 steps higher than G. The low string won't be a problem because it's already down 2 steps, the other 2 however are in danger of breaking if they are light gauge strings, or if they are heavier they may put excessive tension on the neck causing it to bow, never a good thing. This may be possible on a very well built guitar but I'd strongly suggest not going any further than that. From there you'll need to change strings.
Higher gauges
If you're using the 2nd, 3rd and 4th strings you've got, from high to low, B, G and D. If the B goes up one step and the D goes down 2 steps you've got CGC, that's a 151 in C major. From there you can go up and down depending on string tension but not as far as you could previously as the top and bottom strings are going in different directions. You've also got a mismatch in tension between your strings. You may or may not find that a problem.
Heavier gauges
If you use the 4th, 5th and 6th strings, you've got, from high to low, D, A and E. This is easy, take the bottom E down 2 steps and you got a DAD with a big bottom end in it, sounds great. From there you can also go up and down, with the same caveats as before.
Experiment
Sometimes there's just no clear answer to a question and this is one of them. There are so many competing factors that you just need to try things and see what happens. At least if you know what you're doing though you can make informed choices, and hopefully not break anything.