The most important thing is to have a skill but I think I would choose to get the skills before I go for my university education in order to enable me use the skills to support myself financially during my educational period. But if you are from a rich home, before or after wouldn't matter so much with you.
either of the two are important , but for me like what you said? it is Skills is what important before going to university as we can earn from our skills to support our education(we knew how expensive education nowadays.
and also even if we did not succeed in our education at least our skills will feed our family all our life.