To buy some ships like Imperial Clipper, Courier, Cutter or Federal Dropship, Corvette you will need high rank within Major Faction. Here you can read tips on how to progress through those ranks as fast as possible. It's done in build 1.2 and as we know in 1.3 the mission system will be completely rehauled but the base should remain similar.
1. Find a Good System
Federation or Empire System
Very High Population
A Lot of Stations
Dual Economy System (Preferable with one Agriculture Station)
2. Ranking UP
Check which Minor Factions are allied with Empire or Federation
Do any missions for them until you see REPUTATION GAIN missions
Do Naval Progression missions (One mission per each rank needed)
3. Missions
Missions are updated every 10 min
Switch between game modes (Open, Solo and Different Private Groups)
Only Reputation Gain count (Food Needed, Need Covert Help etc.)
4. Mission Objectives
Bring Food, Weapons, Medicine (All kinds of commodities: Fish, Grain, Algae, Food Cartridges, Agri-Medicines, Non-Lethal Weapons etc. etc.)
Illegal activities like Slaves (ignore those)
5. Naval progression
Delivery Missions (Deliver messages, can involve outposts)
Assassination Missions like Kill General, Kill Pirates - all combat oriented ships with bounties (Search for those at Unidentified Signal Sources)
6. Rankings
Empire:
Outsider
Serf
Master
Squire
Knight
Lord
Baron
Viscount
Count
Earl
Federation:
Recruit
Cadet
Midshipman
Petty Officer
Chief Petty Officer
Warrant Officer
Ensign
Lieutenant
Lieutenant Commander
Post Commander
7. Ship
Multi-Purpose - You need a ship with big cargo bay, ready to fight and that can land on outposts.Python would by my top choice, but any ship will do.