Fixed Effects Common Panel Regression versus GMM estimation


I have estimated my model using the Fixed Effects Common Panel method and this seems to work fine. I get an R2 of .90

However, I am now in doubt whether I should use GMM to estimate my model instead? I am not very familiar with GMM.

Could someone tell me what the prerequisites for the choice to use GMM are?

Is it correctly understood, that if my explanatory variables are correlated with the error term, then I should use these variables as IVs in a GMM estimation? Instead of doing a Fixed Effects regression.

Thank you for your help! It is greatly appreciated!