Is the basic reproduction number unique?
It should be noted that many of the methods you talk about aren't necessarily for getting a number but rather a formula for $R_0$, all of which should be equivalent. 

However, when those methods step into the realm of getting a number by fitting parameters, they may give different results as they handle certain aspects of the data differently.

You are certainly "allowed" to use any formulation of $R_0$ you want - just document what you did.