Welcome to the forums and to the game
Ok, I just fired up a 60 - planet clusters map, with two diff 7 vanilla AIs, no minor factions or plots, normal role. Laser gatling bonus.
Sounds like a good start.
Now what in heck am I supposed to do?
For a general list of objectives click on the STATS button near the bottom-left of the screen and then go to the Objectives tab of the window that brings up.
But since you're asking, here's an outline:
1) Do as much scouting as you can and make sure your position is reasonably secure against enemy attack. Build your mobile attack force.
2) Take out the Core Shield Generators. You'll need to kill 4 of the 5 CSG-A generators, and one each of the CSG-B, CSG-C, CSG-D, and CSG-E generators. To kill a generator you need to kill the AI command station on that planet, and start your own station there, and then have your fleet shoot the generator.
- Naturally, you need to find them first, hence the scouting in the first step. Keep scouting through all this unless you've already got intel on all the planets.
3) Take out the AI Homeworlds. You may need to to take more planets to get enough knowledge to get a strong enough force to pull it off. The scout reports on the AI HWs are critical for figuring out how to take them down, as they vary in which "brutal" guard-post (or guard-post-like) structures they get. If you like you can experiment your way through that fight (savescumming probably necessary) or you can ask here once you find out what's on the two AI HWs
And in general there's plenty of advice to be had here for the asking. But the game gives you the info you
need, albeit it tends to still kill you until you've seen it in action enough before.