Here's what I did.
1) if you don't have one...get a type 6 and upgrade it's FSD and whatever else you can afford (PP, PD, Thrusters.. etc)
2) Find a Agriculture planet and buy 10 of each food (Algea, Fruit & veggies, coffee..etc)
3) Visit each of the neighboring systems that are non-agricultural (industrial, refinery, extraction, high tech). Also, buy some agri-medicines and food cartridges when you see them. There are a few missions for these as well.
4) Look for "Need food" missions from minor factions that are
ONLY aligned with the major faction you want to rank up in. Take the mission, give food, move to the next star.
5) Pick up courier missions as well. They are quick one way trips and no cargo space needed. Again, never take a mission from a minor faction that doesn't have the symbol of the major faction (Empire, Federation, Alliance) by their name.
6) Forget any combat missions. They are a huge time sink. Stay with food and couriers.
Do this until you get a Naval Progression Opportunity mission. Do that mission and move about 30-50 LY's away, find another agriculture planet and start over. The reason for this move is because to keep your Major faction rep steadily rising you will "cap out" on rep with local minor factions and you must find new minor factions to raise your rep with. I got to Baron in probably 5 days of playing. I would likely have cut this down a lot if I knew this system going in rather than figuring it out myself.
Happy faction grinding
