Aurora is a bit like an open sandbox. There are no predefined objectives, so we have to challenge ourselves.
Conventional Start: Teraform Mars.
[ ] Research the TransNewtonian base tech.
[ ] Research at least one Cyrogenic module.
[ ] Research Pressurized Water Reactor and Nuclear Thermal Propulsion
[ ] Design and Research a nuclear thermal commercial engine.
[ ] Design a freighter with at least 25,000 tons cargo capacity.
[ ] Design a smaller colony ship.
[ ] Build and expand a commercial shipyard large enough to build your freighter.
[ ] Build about 300 infrastructure (enough for about 1 million citizens).
[ ] Ship infrastructure to Mars.
[ ] Ship 1 million citizens or so to Mars.
((By this point civilian shipping companies should appear and be automatically moving more infrastructure and population. Building and shipping additional infrastructures/population yourself is optional.))
[ ] Build 4 teriforming facilities for every 1 million unemployed workers on Mars.
[ ] Ship teriforming facilities to Mars and begin adding Oxygen and Green House Gasses to the atmosphere.
Teriforming Mars is a relatively simple objective, but may help familiarize the new player with how Aurora works.
TransNewtonian Start: Conquer an Allien
[ ] Research Jump Point Theory, Jump Efficancy, Jump Radius, Jump Squad Size
[ ] Design and build a Jump-Capable scout.
[ ] Start scouting until you find a target.
[ ] Research Missile related Techs.
[ ] Research a beam weapon tech of your choice. Lasers or Railguns are recommended.
[ ] Research Sensor and Armor technology upgrades as necessarily to match the beam/missile tech.
[ ] Research improved propulsion technology upgrades as necessary to match beam/missile tech.
[ ] Design and build beam-weapon jump-point defense ship. (You want these before you find aliens)
[ ] (After finding aliens) Design and build an attack fleet of missile ships with your latest technology. See ship design forum.
[ ] Go squash the aliens. If it doesn't work, identify what went wrong and build a new improved fleet.
This is rather generic and leaves out a lot of stuff required to survive mineral crunches, but can be fun. Possibly Dwarf Fortress Fun.
Any Start: Mineral Prospecting
Objective: Defeat the Mineral Crunch.
[ ] Build Automines.
[ ] Build More Automines.
[ ] Research, design, and build Jump capable survey ships.
[ ] Look for worlds with 200,000+ mineral quantities at 0.7+ accessibility.
[ ] Find such a world for every mineral. Find two such worlds for Duranium. For best results look for worlds with multiple minerals. If you are lucky all of this will be in Sol.
[ ] Transport Automines to mining colonies.
[ ] Continue shipping automines to mining colonies until the mining colonies are producing more of every mineral than Earth.
As far as starting research: Consider using auto-assignment for your first transnewtonian game. Then research whatever you wish your empire was better at.
For self-assignment I typically do the following:
[ ] Buy the next level of every missile upgrade.
[ ] Buy Pebble Bed reactors and Nuclear Pulse engines.
[ ] Buy a level of fuel efficacy and maximum engine power.
[ ] Get Jump Point Theory and either jump gates or the basic jump drive techs.
[ ] Buy the next level in every sensor.
The rest of the tech points might be spent on further engine upgrades, fighter related logistics, shields, beam systems, or construction rate improvements depending on what I want to do with the empire that game. It changes every time.