Historical: Wars of the Republic Era -> Era Digest: Dark Age -> Era Report: 3145 -> Field Manual: 3145
At least, that is what I would suggest.
The Historical doesn't have so much on the Periphery, but it makes some of the things in the ER make much more sense.
To add to that list, I'd also advise reading
A Bonfire of Worlds before getting around to
Field Manual: 3145. Or possibly even before
Era Report: 3145.
If for nothing else, the introductory story fiction in
FM:3145 works a lot better after reading one of
Bonfire's plot threads in particular. (The relevance of said plot thread may not be immediately apparent from a Periphery perspective. But I suspect that the impact of those events will eventually spill over beyond the edges of the Inner Sphere once the storyline starts to move past 3145.)