i had the same problem, I think everyone else did too -- so here it is: A campaign guide that worked with plenty of elbow room on normal, so I'd guess it should be good for another difficulty level or two.
Use your campaign funds, the ones you start the mission with. Do not attempt to create revenue (that's only necessary, at least on normal, on one mission or less). And use them quickly -- buy the first, and maybe second factory on any planet colonized, IF the planet is necessary. Buy any necessary colony ships.
Keep your social production at 100%, industry at 100% until you have enough research stations (basic labs are good, xeno labs are also okay) to grab planetary invasion, enhanced miniaturization, basic or enhanced logistics, impulse drives (I like mark II, it's small and cheap, and Mark III is good if you really need it -- Warp makes it easy -- unless they run up and slaughter you first!) and some guns. If you have the option -- you SHOULDN'T in most missions -- gain warp tech and construct a chain of starbases with the +1 speed modules to ferry your death buckets to their final destination. Then switch from research to military, maybe with a quick stop on social if you need a few more basic factories. Keep morale at 100%, you'll need the population for invasions -- and move the population as close to the objective as possible to speed it up.
Plasma is excellent, you can put two of them on a tiny, but it won't be useful against long-range targets with no engines... I once used Plasma MkIII's on my small hull ships along with a warp mk1, but it was a very close game. It was what I'd say was the hardest level, the one where you have to destroy 4 dread lord worlds. Just glue some really bright flashlights for weaponry and spray cans for engines onto some space coffins and launch them -- as long as you can build ONE PER TURN, you're pure gold.
Necessary planets are: Those that expand your range to reach and complete the mission objective, any with incredible production/research bonus tiles (cheese alert! But hey, *I* want to scout a planet before I disassable my colony ship! Who wouldn't?), but generally, you need to avoid aquiring planets! The 12bc mantenence really adds up, and that's without any constructions at all. They're harder to destroy than starbases, but starbase construction ships only cost what, 1,000, 1,500 bc? And that's just if you can't focus on military to produce one quickly enough.
In any case it's not so much what you do in a mission, but what you DON'T do that makes the difference. I finished the final mission by simply making a transport and throwing it at the DL world. It was almost like they were surrendering.

In the one previous to that -- I can't recall the names -- you start with an incredible supercapital vessel. Sell it. Hahahahaha! Sell it to the Altarians! Hahahaha! It takes most of your treasury in maintence by the end of the mission, will never be upgraded, and it's powered by a team of people with space-oars! And a dread lord escort ship would still smear it across the cosmos!