tinyE: Hey, kind of OT.
Do you need to play those in order?
I could never get into #1 and 2 but I've always been really curious to try #3 even though I am so awful with TBS.
There are some references and some recurring characters, but you can pretty much start from the game you want. Fallout 1, Fallout 2 and Fallout New Vegas share the same development philosophy and some of the developers. Fallout 3 and Fallout 4 are made by Bethesda Game Studios, and are a bit different (less focus on character development and quest design, more focus on world design, exploration etc.). A lot of the hardcore original fans tend to hate 3 & 4, but I think they were pretty good (Fallout 3 is actually one of my favorite games ever).
Fallout 3, Fallout NV and Fallout 4 are not turn-based, they are first (or third, but this mode kind of sucks) person action games and feature something called "VATS" which gives you the possibility to slow down (or stop, depending on the game) time, but they're real time :)