How can I set a Pick and pack price for an order in my site?

You can add Pick and Pack charge in shipping method, here you will see an option of Handling Charge. You will find this option in Admin > Preference > Shipping > Methods > Edit > add Handling charge
Another option  is to add the Pick and Pack charges in the pricing engine, the calculator pricing engine allows you to add different option and you can include Pick and Pack option. In pricing engine you can hide this option from user, if you don't want the user to not see this charge by adding it in Calculator Parameter and set show as an option to No.