I have finished the story. I have purchased the biggest/baddest ship in the galaxy (BLACKGATE) and I am now relaxing, cruising around harvesting and still looking for those all elusive alien hardware gear drops. So, since first officer has the con and I'm lounging in the captains bunk, I figured I'd write some general experience and tips down for others interested.
1. Don't rush to the story missions. The difficulty of all missions (including the story missions) is relative to your 'installed upgrades/components'. The type of ship only matters in so far as some have more turrets/broadsides/component slots but it is actually the level (MK1, MK2, MK3, etc. etc.) of each installed part that determines a mission's overall 'difficulty rating'. I finished the story game using a ship (ICARUS) which was still a corvette class (like the starting ship) but had 2 more turrets than the starting ship. Of course I upgraded the ship as I went along (spent several millions of credits doing so) and had to use speed and tactics to defeat the larger vessels (frigates, destroyers, dreds etc.) encountered.
2. When you are in the map (sector map by hitting SHIFT) check for system difficulty. I always chose to hang in the one's with EXTREME difficulty because the chances of better loot drops seemed increased. Of course this was frustrating at times due to overwhelming odds especially vs the larger more heavily armed ships but if you're careful you can control how many enemies you 'pull' from a mob and can whittle them down one by one.
3. Especially in later game you will get pulled out of warp a lot. This gets insanely frustrating. I inadvertently found a bug. If you hit M (map key) to go to map just as you're about to have to exit warp (either due to an asteroid field or enemy ships etc.) and then hit it again to zoom back to your ship you'll have skipped past 'the danger'. Especially helpful during long merchant mission drops etc. where getting pulled from warp 5 times in 45 seconds just to skip around an asteroid field or to dispatch some low-level mob is just frustrating to say the least.
4. Put money into shields (of course) but also engines and boosters. Once you get to the RADOVICH (Hauler accessible through the merchants guild) you're in the easy money. I put null-grav boosters on the RADOVICH, an MK5 shield and an MK5 (must be MK4 at least) deflector and ran almost exclusively dead-drop missions for 1 or 1.5MIL credits a piece. All without firing a single shot from the broadsides. Talk about THE blockade runner in the game. Warp in, the enemy inhibit your engines, you null-grav boost up to the station anyway and done. Obviously you should have lots of flak turrets by this time and that MK5 deflector comes in handy keeping you alive while the null-grav re-charges.
5. Always grab the missions from the highest level of system you can survive in. Usually the best (most lucrative) missions spawn at the respective 'guild offices'. If you don't like what you see, grab them all. Exit the station. Re-enter the station. Go to your missions and drop them all, then check for new missions. Rinse and repeat until you find that mission of a lifetime!
6. Once you have about 20MIL credits (the BLACKGATE is about 16MIL) you'll have enough for the BLACKGATE and at least some late-game turrets/equipment. Get it and enjoy cruising around 'melting the galaxy'.
So far I have only captained the starting ship, the ICARUS (the ship I 'finished the game' in), the RADOVICH (the money-maker for me), and now the BLACKGATE. I will try some of the others with different loadouts now that I'm playing in sand-box mode.
Some potentially helpful links I found:
Visual list of player ships in the game:
http://imgur.com/a/QaJho
List of ships and their costs (although I think some costs have been tweaked by the devs since this list):
http://rebelgalaxy.gamepedia.com/Ships