I have just finished my course on England in the time of Richard III with Future Learn. Quite suitable, on the day after his reinternment in Leicester cathedral. If you did not manage to see anything - and is interested - you can watch some key videos here.
It was an interesting course, very accessible, meaning, not too academic. Mixed with texts, videos and discussion forum, it covered the whole range of society, food and living habits, clothing, manuscripts, religion and in the end the whole fantastic story of how the grave of Richard III was found, in a car park in 2012. Philippa Langley was the person behind the quest, and she wrote the book The Search for Richard III - The King's Grave together with Michael Jones who added the historical background to his life (review here). I will visit England in April and will definitely put Leicester on my itinerary.
The course also opened up my eyes to all the fantastic archives that are now available on-line. That will be something to explore further.
I have still not read Shakespeare's Richard III. However, I now know he was biased by Henry VII and his times to put Richard III in a bad light, but that means I have to read it with an open mind and compare his text with what I know now.