Feature Selection with non-linear numerical and categorical variables

I have a dataset of 45 non-linear numerical values and 2 categorical values. I am making a feature selection to predict categorical variables one by one or together. I used the correlation ratio and kendall rank correlation coefficient to calculate the strenght of the relations.

Among these two methods, which one should I use as the primary method to sort the strenght of variables? For example the table below is sorted by correlation ratio. Should I sort the table with the kendall coefficient instead?