I have been meaning to watch Peaky Blinders.
Also I am interested in Broadchurch but don't know if I should watch the UK version or the US version or both.
I was thinking of watching the Flash, Arrow but then would require watching Supergirl and Legends of tomorrow because of all the crossover episodes.
I watched the US version of Broadchurch (Gracepoint) and then the original UK version. I recommend watching it the other way round. There are some creepy similarities between the two versions, especially the early episodes in the sequence, but eventually there are big differences between the two stories and the characters. They were made for different audiences so it is fun figuring out why they structured each story the way they did. I find that in Australia we can appreciate both sides of the story, however some people in the USA wouldn't appreciate or understand the UK version or vice versa.
I was watching the UK version and saw a scene which was set indoors. In the US version this equivalent scene had taken place outdoors. My prediction was that bad weather had affected the UK filming and the scene had to be moved indoors to fit in with the filming schedule. Later I saw some behind the scenes footage which confirmed my theory.
The ironic thing is that the US version is actually filmed in Canada. I figured this out by looking at the architecture of the houses. They looked similar to the houses in other shows which are filmed in Canada but set in the US.
As for Arrow, Flash, Legends of Tomorrow I suggest you watch them in the order they were screened in the US. Many of the characters in Legends of Tomorrow are established in Arrow and Flash first so Legends doesn't make a lot of sense until you've watched the relevant episodes of the other shows.
I watched Supergirl out of curiosity and eventually found I liked it. It's possible to enjoy the Supergirl episode which guest stars The Flash without having seen any of the The Flash episodes but there are a few bits and pieces in the story line which only make sense if you've seen all of both shows.
As Supergirl and The Flash were on different networks at the time the storylines which linked the two shows together didn't quite match up. The order the episodes were aired in Australia made more sense than the US screening order. The networks attempted to align their schedules but last minute changes meant it didn't quite work.