Each Fallout game is unique and has its own interesting aspects. You don't have to play the previous ones to enjoy Fallout 4. And yes, the Shoddycast series about the Fallout Lore is amazing! However, if you would like to find out some of the backstory yourself, I would highly suggest to get the other Fallout games as well.
Fallout 1 and 2 take you way back to the beginning of a lot of the Factions. Those are from around 1997 and are top down, isometric view games. Sure, not everyone's cup of tea, but they have an immense story value. Really well written dialogue and characters.
Fallout 3 takes place in/around Washington DC and the area is still heavily irradiated and damaged. There are some really interesting locations that you can explore.
Fallout New Vegas takes place in the Mojave around New Vegas, Nevada. You can actually visit the Hoover Dam. The story is brilliant, you have a lot of choices to make and not all will be easy. It has the best DLCs, so far, in the Fallout franchise (at least for me). It's one of my top 5 all time favorite games, because not only do you have a lot of freedom here, but you really have to think about your actions, because they do matter!