No this is not a tutorial on how to pick a song, say for a party. And also it is not a tutorial on teaching people about good music - although it gives a good indication. But this is a tutorial on how to choose a great song to showcase a band's talent to their fullest potential...

If you think about a gig, there are so many things to get right - I have had personal experience - like DJ machine failure, technical failings, singer has a bad throat and suddenly you find the need to go to the toilet in the middle of our performance. But if you set those aside, which you should do if you are serious, then there is only one real problem song selection.
Instantly the "aware" one of your band will shout "think of the audience" which I totally agree with, to a certain extent, but it should not be your first thought. Instead you should think about yourselves. Who is giving the performance? Well you guys (or gals). So it is more a question of what will you like to do. If you simply a play a song for the sake of being liked then you become no better than the rubbish "pop stars" of today, not naming anyone. But if you choose a song simply on the premises that it is such a relaxing (or energetic) song to play that you like playing it.
The second you have that done, your band will have chosen the best song possible - for my band it is more ballad based with more reverb and funk than distortion and roars. In the end, we played some awesome songs which people liked because we played it well - not playing something they like badly. So I hope you have gained something from this, it is like a life lesson but for musicians - sort of like a dude which I met after the gig, but that's another story...