You can also see JM Wooldridge Econometric Analysis of Cross Section and Panel Data.
It is best for you if you follow a testbook by doing econometrics with a software. Princeton used to have onlne spme tutorial on stata. A youtube channel econometrics academy I think was called had also some tutorials with codes
I'm not trying to be picky, but just in case, there is no such thing as the consistent but inefficient estimator. Perhaps you mean a consistent but inefficient estimator?
Your estimator is the OLS estimator. See $X'X$ cancelled.
If you only use the moment conditions $E(x_t u_t)=0$, then OLS is the only GMM (or actually MM) estimator that can follow. As the ...