There are many effect size statistics for ANOVA and regression, and as you may have noticed, journal editors are now requiring you include one.
Unfortunately, the one your editor wants or is the one most appropriate to your research may not be the one your software makes available (SPSS, for example, reports Partial Eta Squared only, although it labels it Eta Squared in early versions).
You have to be careful, if you’re using SPSS, to use the correct values, as SPSS labels aren’t always what we think. For example, for SSTotal, use what SPSS labels SS Corrected Total.
What SPSS labels SS Total actually also includes SS for the Intercept, which is redundant to other information in the model.
The denominator for Cohen’s d is always some measure of standard deviation. I’ve shown s pooled here, but you often see different options, including just using one sample’s s. This is the one I see used most commonly.