Partial eta squared is overwhelmingly cited as a measure of effect size in the educational research literature.
Use the square of a Pearson correlation for effect sizes for partial η 2(R-squared in a multiple regression) giving 0.01 (small), 0.09 (medium) and 0.25(large) which are intuitively larger values than eta-squared.
On the one hand, partial eta-squared is an easily interpretable and straight forward measure for the effect size. It gives you the ratio how much of the total variance in your sample can be explained by the factor you are interested in.
However, the emphasis here is on "in your sample". Eta-squared only compares the calculated variances of your sample and doesn't correct for the degrees of freedom. Therefore, it overestimates the "real" effect size in the population. Instead you can go for Omega-squared, which does this correction and therefore is less biased.
In the first step, you need to specify your goal. If you want to know the percentage of variance which be explained by factors, you can use Eta-squared.