I began a game of SRM Season 2, which is the first 4th Edition season and the game is set in Denver. Season 3 is set in New York, Season 4 is set in Seattle, and Season 5 is set in Chicago.
If I were in your shoes, I would begin with Season 4, using the example characters in the book for the players to confuse yourself and your players as little as possible. The biggest changes from my point of view between 4th and 5th is, in no particular order, the entire Matrix system, direct combat (initiative, weapon stats, armor, etc), and various tweaks and fixes made to other aspects of the game.
I personally think that Season 4 sets up Sprawl Wilds, Firing Line, and Season 5 beautifully, and I enjoyed reading the fluff. There's also an absolute wealth of information on Seattle, since it's the icon runner city, whereas Chicago (aka Bug City) is a feral city not really representative of most of the world. I would personally imagine that the Season 4 Seattle campaign could be played much more diplomatically than a potential Chicago campaign, as you just can't reason with insect spirits.
Summary;
Read Seattle 2072 while your players read up on each piece of gear and rule affecting their chosen example characters for Season 4
Play Season 4
Play Splintered State
Retire the example characters
Create new 5th Edition characters once the Errata has been released
Play Sprawl Wilds, Firing Line, and then SRM Season 5