How to choose a distribution for the likelihood step?

I could plot the joint distribution using Seaborn. I could get the figures I needed. I am thankful for your responses.
Currently, I am trying to work on fitting the parameters of Norma-gamma distribution. I was trying to use MLE. But i found that the initial guess affects the final results. Is there any established rules or thumb rules for the initial guess? Or can i consider the initial guess using method of moment?
Thanks in advance