Dude, no offence but you are overthinking this
Aurora is complex but it isn't THAT complex! You'll learn and re-learn the game as you play, there's no need for a study plan or anything like that. You learn each system as you come across it or need it. Don't stress it.
You should build some sort of Battle Fleet before you leave Sol but the details are largely meaningless. That is because of the immense random element in play, though you can reduce its impact via game options. It is possible to get really unlucky and meet higher-tech spoilers just 2 jumps from Sol who then wipe your civilization out in short order. Or you could survey 100 systems without finding hostiles. Some NPRs will hate you almost immediately while others are easy to befriend. So any advice regarding the technical details of your first battle fleet is largely meaningless because you cannot know what sort of opposition it'll go against.
But the rule of thumb is that a well-rounded fleet can at least get you information about the enemy before having to retreat or getting destroyed, and JP defence can be done successfully even if outnumbered and -teched. Combination of fast ships with plasma guns and slow box launcher missile platforms at each Sol JP is generally enough to wipe out any enemy ship(s) coming through unless you're really unlucky. That buys you time to design and build better ships, ones that are tailored to defeat your enemy. Oh and a well-rounded fleet means that you have a bunch of specialist ships that support each other, so for example:
1) Command/sensor ship (could be a carrier carrying recon fighters)
2) Missile launcher ships
3) Beam attack ships
4) Anti-missile missile launcher ships - AM escorts
5) PD escorts ships (either lot of railguns or gauss turrets)
That does not guarantee victory but it means you can try different approaches when you encounter hostiles.
There is no hard and fast rule regarding turtling in Sol or exploring quickly. If you start with no NPRs, then turtling in Sol to improve tech and building up your industry is totally safe. Exploration is always risky; on the other hand, you must do it to find more minerals. But again, the random element is big so there are no specific thresholds. Neither are there any critical technologies without which you should not explore. Obviously, you need jump engines and gravitational survey sensors to leave Sol in the first place. Having shields on top of armour is also useful and the faster your engines, the better in general. But when stuff gets spawned, some of it depends on your size and tech level (in a very rough manner) so there is a downside to just doing lot of research before venturing forth.
As for strategic planning, there are few general hurdles that most campaigns have to overcome though they do not always happen in the same order:
1) Mineral crunch - Earth runs dry, you can't find/mine/transport enough minerals in a timely manner back to Earth. This is almost always the first problem. So getting your mining industry up & running is generally the first strategic goal but it is also something that always requires some attention. This then pushes research and exploration and colonization and fleet logistics.
2) Fuel shortage - once you start having a bunch of ships, fuel becomes the next issue. So get some harvesters to the gas giants and a tanker or two running the rounds delivering that fuel. Remember that a tanker with a refuelling system can only GIVE fuel, it cannot TAKE fuel from a ship/station, so your Sorium harvesting stations need a refuelling system of their own so that they can fill up tankers that can then take that fuel to other ships and colonies.
3) Financial crisis - especially with a TN-start, wealth can become a big issue. Solving it requires lot of financial centres and having civilian shipping lines can also help a lot. So, you need colonies on Luna and Mars to stimulate civilian growth which brings more tax wealth to you. You might need to cut spending down, not buying minerals from civilians or not building so many ships.
4) Due to the new ground combat model in C# Aurora, if you ever decide to invade an NPR home world, you need a big army. And I mean A LOT of troops. Not some piddly amount like Allied forces at Normandy beaches on D-Day, no. We're talking about Red Army in 1944 humongous size. Or Warhammer 40,000 Imperial Guard. That means you have to start researching ground forces right from the start and start building them as soon as you can. There is a huge temptation to wait until your tech gets better and focus on specialized training but that would be a mistake. Yes, there are cases where you need specialized training and there are small-scale ground battles but for NPR homeworld invasions, you need massive numbers of bodies and metal.
Finally, just have fun. You will lose a bunch of games, don't fret about it. Each game is a learning experience too!
