#1 and #3 would be natural answers to the question 'What do you do for a living?'. The second one wouldn't sound natural.

All of these are fine answers. Language is fluid and for how you express yourself, there isn't always just a single answer. This is contrary to what many language textbooks or even teachers have students believe. Of course, there are rules for grammar and vocabulary and you should try your best to abide by those rules, but as long as you are communicating your ideas clearly, then that is what is most important. All three of these sentences are simply three different ways of expressing the same idea and are all grammatically correct as well.