There's three stages to aurora far as I can see.
Researching/Building/MiningIf you lack a CP and/or PP scientist, immediately build 3-4 Military Academies. I just quit a game because I had dink all for scientists in the first 25 years. (Although this isn't a game killer, the longer you play the bigger NPRs get, and the longer each turn takes to process)
Get your Research rate up, mining rate up, and train (give them a project and a lab) 1 scientist in every area except perhaps logistics, biology and energy weapons (if you're not intending to use them). Geosurvey sol, find what minerals you have and start mining/mass drivering them back to earth. Start working on engine efficiency. Ion drive + 0.5L/hr is plenty to aim for when it comes to commercial ships
Minerals of importance: Corundium (mines), Mercassium (research labs), Sorium (processed into fuel, but you need raw Sorium to make jump engines/gate builders), and Neutronium (primarily used to build shipyards/increase their capacity). Depending on your luck Duranium may be an issue (this is used in everything, so you'll need it in bulk). Claim comets/asteroids that get surveyed with 10k+ of these minerals (excluding duranium unless you're desperate), and claim all colonizable/mineable planets/moons to stop civvies from mining it away from you. The economy boost is small, and the minerals are gone for good.
Ships: Geosurvey (design and build this right away with whatever engines you can make), Cargo ship
Colonization/Expansion (Be ready for military demands from colonies at this point. Easy to handle, but annoying if you're not expecting it)
Research to get a military setup running. Pick and choose your weapons so you're not behind the tech curve when you find an enemy. Luna and Mars are easy to colonize for the extra wealth you'll need to run your research. Expansion into other solar systems directly linked to earth is easy and unlikely to run you into nasties, but the chance still exists.
Ships: Colony ship, grav survey ship, jump gate ship, geosurvey self jumping ship, tankers to harvest fuel from gas giants, token defense ship to shut those colonists up.
Conquest/CombatYour tech + minerals should be coming together to form your fleet. Missile cruisers + point defense? Laser fleet? Up to you really, they all have benefits and problems. Missiles are very powerful though.
Ideally (In my mind) this stage should be ~50 years after start. Namely because the longer you leave NPRs, the more NPRs they spawn and the slower your game plays as a result. NPRs fighting will cause 30 second timelapses that take longer than 30 days did at the start of the game. If there's fighting going down, it's much more fun to be involved rather than sitting and knowing shit is blowing up but you're not involved.
Many minerals gain new value in the end game. Duranium obviously never changes from being needed in bulk. All military ships require an upkeep of the mineral types that went into building them.
Everyone needs
Gallicite(engines)
Tritanium (engines)
Uridium (sensor clusters)
Corbomite (shields)
Depending on your weaponry you may need:
Gallicite (missiles/launchers)
Tritanium (missiles/launchers)
Processed Sorium (missiles use fuel as well)
Vendarite (gauss cannon)
Corundium (Laser style weapons)
Boronide (Laser style weapons & railguns)
Neutronium (railguns)
If you're having trouble with step one, honestly aurora might not be for you. The game is for people who love complexity and there's really no "quick and easy howto" that can exist because of that. If you're having trouble with combat and where to go with military, there's a great (albeit slightly outdated) post here
http://www.gamerswithjobs.com/node/48620?page=13It really helped me clear up the strengths/weaknesses for weapons and decide on what to aim for with military.