First of all - this is a work in progress. I guess i'll update this whenever i play a notice something.
I've now played a total of 4 galactic conquest (easy on both sides, medium imperial, hard rebel) and just wanted to write down some experiences.
Non side-specifics:
Though it may seems that you start of with plenty of credits, be aware - those are used up quicker than you think. You need to quickly increase your income, since taxation and mining income won't finance your needs alone. You have two choices - either you quickly amass a strong force in one corner and try to conquer several planets to increase your income, or you stay defensive and build a transport fleet. Which way is better is usually decided by the map you play. Some maps, like Galaxy Far, Far Away as Imperium give you a great position in the top left to quickly gain two Planets with Mining 5. Both combined with Mines bring over 20k Credit income. If you do not have such a worthy prey, you should consider going the defensive way and first incresing your transport fleet, then using this income to upgrade/build an army.
Usually it's always best to focus your attention on one corner of the galaxy. Find a corner where you have a high tech planet (high shipyard, a lot of ground space) and build a fleet and army. All other planets should receive less attention, only increasing their defensive fleets. If you do not focus your attention, you will end up with a lot of frontline to cover with little troops. This way you usually only have to defend 2 or 3 planets, while several others behind are save from enemy attacks and do not require standing fleets.
Imperium:
Your primary goal should be to research the CTF Container Transport (Shipyard 2, Research Station) and it's upgrades and build a fleet to increase your economy. This unit will greatly increase income. Mining worlds should only have one production building and the rest mines. Since the Imperium lacks strong ships in the beginning you should start researching new classes. Usually a good combination is upgrading the Acclamator for shipyard 3 and the Imperial Class Star Destroyer for Shipyards 4. While the Imperial is your true frontline warship, in greater numbers (and tech) the Acclamator's high torpedo yield allow it to fend off even far superior opponents, helping your non-connected low-tech planets stay save. Since it takes a long time to research and build those ships it is advised to upgrade your heroes (Thrawn for example). This may have a high cost, but their ships are worth a small fleet. In the Galaxy Far, Far Away setting an upgraded Thrawn combined with his starting fleet can destroy all ships in the top left corner, leaving you with several easy to conquer planets with a high mining level.
The Imperium focusses heavily on walkers, so your main ground production building should be Walker. The AT-AT is an incredibly durable unit with an acceptable damage output and can serve as your frontline unit. You still need to support it with fast attack units, else he can easily destroyed by faster units, since his turn speed is slow. Upgrading gives you a very durable and long ranged unit that has a low cost in space and tactical population, therefor maximizing the population usage.
To keep planets with low Tech (less than 4) save from attacks by capital ships, it is incredibly useful to built a Hypervelocity Gun. On worlds with higher shipyards, building a bigger defensive fleet is usually more effective.
Rebel:
The Rebels do not have such a great Transport (MCF Modular Conveyor is good, but not as good), so it may be even better to simply go for a more aggressive strategy. Unlike the Imperium, with the Recusant they have a formidable ship straight in the beginning. This ship can deal with all kinds of enemies and has a good range on it's main weapons. If upgraded it gains an experimental Turbolaser - the longest ranged weapon in the game. Simply massing a fleet out of those - though costly - allows you to deal with all kinds of enemies. Combined with the Armored Freerunner as ground unit you have starting units that can easily conquer planets. The Armored Freerunner greatly scales with upgrades, packs a strong punch and since is a landspeeder is great for hit and run tactics, repairing the damaged units.
Counterintuitively the strongest spaceships for the Rebels are no huge capital ships, but Frigates, or more precisely the Assault Frigate and the CC-9600. The Assault Frigate is similar to the Recusant - a jack of all trades - it costs vastly less tactical population and credits, while being almost as effective in combat. The CC-9600 on the other hand is virtually defenseless against Fighters, but if upgraded it becomes a platform raining death down on any capital ship. The low tactical costs combined with their armament essentially allow yourself to field vastly superior forces than your enemy, but on the other hand mean you have to use more micromanagement to keep your fleet alive. Quick strikes by the Assault Frigates under Cover-Fire from CC-9600s, then fall back and replenish shields. Each of those attacks should easily destroy one or more enemy ships without resulting in casualties. Combined with a high salvage percentage, simply "roaming" the galaxy with such a fleet can provide a nice income while greatly weakening your opponents offensive capacity.