The human voice is very malleable and can be moulded any which way with proper training. The human mind, however, is a tricky beast. It gets easily discouraged and frustrated. Therefore, with respect to singing songs to start with, the rule that works best is :

“Start simple and build on it “. 

Your vocal coach will be your best guide in this. The first step to this is analyzing your voice. It is as important to know your strengths as it is to know your weaknesses. Once you are able to identify these,   you can then start picking songs that fit your current vocal ability and bring out the best in your voice. Say for example, a person who is unable to move quickly between notes, should pick a song that has more straight notes than picking a song which requires a lot of complex movements and modulation. A person whose current range is limited should pick a song within his range . Pick songs that are physically comfortable and you relate with well. Pick songs where your voice texture shines, where your sound is pleasing to your ear and where you look and feel comfortable singing them. 

When you hear the strengths of your voice in its best current ability, it motivates you to expand your horizons.