the games and the show are like unrelated. it just takes place in the same world. if you do want to play the games, Fallout 4 is probably the easiest one to start with for a modern player, and the gameplay is the most approachable, but the story isn't very good. if you have a tolerance for older, slightly jankier games, New Vegas is one of the best games ever made. Fallout 1 and 2 are also great but they're a totally different style: isometric RPGs like Baldur's Gate.

4

Just watch the show, it’s brilliant!

1

You would be completely fine watching only the show. But you may miss some of the references in the show that correlate to the game

1