Did make this : https://www.mmo-nomad.net/fe/APs/Sector 1 AP Missions.pdf (Cleaned up a version I had that was made in 2010).
Edit : https://www.mmo-nomad.net/fe/APs/Sector 2 AP Missions.pdf Sector 2 done.
Edit 2 : https://www.mmo-nomad.net/fe/APs/Sector 3 AP Missions.pdf Sector 3 Done.
And 1 that has all : https://www.mmo-nomad.net/fe/APs/Sector 1-3 AP Missions.pdf
It's a list of all AP Missions you can get in Sector 1. It shows who you need to talk to to start the mission chain(s), and who gives the AP(s).
My recommended way of doing sector 1 is : The starter town you chose (Clinton Farm, Boneclaw or Midway), then these towns:
Odenville, Embry, Oilville, Linewood, Needle Eye, Kingman, Rest Stop, Coppermine, Mowbray, Pinkston, Pass Chris, Watchtower, Trailer Park, Trumbull and Spider Hill.
As to the last 2 starter town and the rest of the old starter town around Embry/Odenville, they can be done at any time.
We also have this showing all AP missions in Fallen Earth : https://fallenearth.wikia.com/wiki/Category:AP_Missions
There are also AP missions in Deadfall, Terminal Woods, Alpha and Outpost, but by now most have what they need to make a build, and AP injectors gets available at level 50 from Dome.