A few days ago I finished Penumbra, the final of the four epic mission arcs.
One of my long term goals is to have is high standings with all four empire factions. The time I started the standing repair plan my gallente standing was about to hit -5.
These standings were with the connections skill at rank 3
Caldari State 8,66
Amarr Empire 5,6
Gallente Federation -4,71
Minmatar Republic -2,96
I started by completing all tutorial missions and did datacenter missions by turning in dog tags and running the courier mission chain. Of course I did storylines in between as well though I should probably avoid doing those in the future.
Faction standings before I started the 4 epic arcs with connections 4
Caldari State 4.64
Gallente Federation 3.78
Amarr Empire 3.72
Minmatar Republic 3.54
Faction standings after finishing the 4 epic arcs, the SoE arc (Minmatar variation) and training connections 5.
Caldari State 5.68
Minmatar Republic 4.91
Gallente Federation 4.66
Amarr Empire 4.52
Training connection skill rank 5 my caldari standing went from 5.5 to 5.68.
The Blood-Stained Stars was done in a nighthawk, previously a hawk was used. Next time I'll try a crow. That should speed things up nicely 3 months from now. Combats are mostly against noob frigates and most time is spent warping around anyway.
Totally off topic, ships will travel faster as a result of the warp changes. This would allow fleets to move around faster if titan jump bridges are ever nerfed in a far away future.