Planning a trip from London -> Edinburgh! Tips on things to do in between much appreciated!

Hello! As the title says, my partner and I are planning a trip to the UK! We would like to fly into London, make our way up through England and Scotland, and fly out of Edinburgh! This will be our first time to the UK so any tips are much appreciated! My main question has to do with transportation - what is the best way to travel throughout the country? By train or by bus? Also, what are some towns that you would recommend stopping at when traveling through? We plan to be in the country for about 10 days. We will probably spend 2 to 3 nights in London and 2 nights in Edinburgh. So that leaves 5ish days to spend in between! Any suggestions welcome!