Watching order for "Toaru Majutsu no Index" and related anime
Having just watched them out of order (accidentally), I highly recommend watching them by order of release date, including the movie.
The original and spin-off series were produced by the same company. (The same team as well I believe) and never aired at the same time.
This makes the recommended order:

Index season 1
Railgun season 1
Index season 2
Index movie
Railgun season 2 (S)
Index season 3
Accelerator season 1
Railgun season 3

Enjoy!