When would you use feature optimization method instead of exploratory analysis to identify best features?

I have a dataset with around 70 features. I'm currently just plotting graphs and trying to identify key information. I also wish to later do a predictive model.

What would be the best way to get the best features?

Would it be wise to go through every column and try and spot trends and correlation? Or would it be sensible to just use a wrapper method or genetic algorithm search?

Or just do a random forest classifier on the whole dataset and them look at feature importances and pick the most important ones?