Because "recently" is a specific time marker, you would use simple past, just as you would with any other time marker. For example:
Recently I read a book about turtles.
I saw my brother recently.
Yesterday I ran to the store.
Last week I visited my mom.
NOW, if someone asks you a question in the present perfect such as, "Have you seen your mother recently?" you may also answer in the present perfect: "Yes, I have seen her recently." But you may also answer "Yes, I saw her recently." and it conveys the same meaning. I hope this is helpful!