I am no expert, but have done both the old and new courses.
All of what you need to do is web based through wordpress, there are some things that can be downloaded to help you if you choose, but the major concern here is your web browser. Chrome if you are on PC and Safari for Apple. (Please someone correct me if I’m wrong, but it works fine for me).
As far as I am aware, carry on as you were, all should be good. Don’t forget to back-up and transfer all your files/images etc. to the new computer. Also remember to update your plugins in WordPress, there was recently an update for the Vacation Soup plugin.
Good luck and feel free to ask on here if you have any questions.