I suggest you should determine both the ARMA and the GARCH parts simultaneously. If you determine the ARMA part first by temporarily ignoring GARCH, this will lead to inconsistent ARMA parameter estimates (unless the MA part is missing) and probably suboptimal selection of autoregressive and moving average lag orders -- because ACF and PACF confidence bounds will be invalid given the neglected GARCH-type residuals. Also, the Ljung-Box test will not have the regular null distribution under GARCH-type residuals, thus you cannot rely on it for testing how well the ARMA model captures the patterns in the data.

These issues have been discussed in earlier posts here, here and to some extent also here.

I suggest you should determine both the ARMA and the GARCH parts simultaneously. If you determine the ARMA part first by temporarily ignoring GARCH, this will lead to inconsistent ARMA parameter estimates (unless the MA part is missing) and probably suboptimal selection of autoregressive and moving average lag orders -- because ACF and PACF confidence bounds will be invalid given the neglected GARCH-type residuals. Also, the Ljung-Box test will not have the regular null distribution under GARCH-type residuals, thus you cannot rely on it for testing how well the ARMA model captures the patterns in the data.

These issues have been discussed in earlier posts here, here and to some extent also here.