Shakespeare history plays

[Star555]

I have been a huge Shakespeare fan since my school days but have not read/seen many of his history plays. I only read and watched Richard III and Henry V as an adult and absolutely loved them. I plan to read and watch more of them this summer, and give myself a well-rounded "education" by also reading about the historical background, other relevant works (fiction/non-fiction) about that time period, etc. My plan is to complete the first tetralogy in order -- starting with Richard II, then Henry IV parts 1 and 2 (already read Henry V). Is this a good approach?

After reading the plays, I plan to watch two adaptations: BBC's The Hollow Crown and RSC's productions directed by Gregory Doran.

I spent most of my childhood school years as an expat in the US, so unfortunately I did not learn British history in depth at school, and didn't have immersive childhood experiences like visiting the Tower of London, etc so my "intuitive" knowledge of British history is shallow. Are there any good fiction/non-fiction books that would go along well with Shakespeare's history plays, to help "fill in the gaps" and provide context? It's ok if they are targeted towards a younger audience. As I said, I didn't get the full dose of British history in my American school (I didn't know that 1066 was an important year until my late teens!) so I don't mind reading children's books now to make up for it! Thank you for any suggestions/advice.