I haven't focused on military techs in early game. In some other gifted games, I had to defend myself even earlier than this. But luckily, a United Planets meeting happens, and they end all active wars for 26 turns. That indeed was a lucky strike for me. as I have more time to prepare for war. With my strong research and upgraded planets, I can now focus on defense first and stepwise, on offense.
First, "we'll need a bigger boat" to deal with these shadow sharks. It would take me 19 turns to research medium hulls. Lukily, the Meklar are so "kind" to trade with me:

I have to trade them an arm and a leg, but we get mediums hulls.
I think it is pointless to go to war with anyone before having mediums hulls and planetary invasion to actually invade planets.
The following event comes... unexpected:

The vampires are giving me planetary invasion. For free!
I'm still working on balancing out the AI settings for this custom faction. In my last game, they were extremely pissed at me though we were both pragmatic races at that time. Had to kill them early on. I wanted to have them as really pragmatic, neutral race (I know you could go the "evil vampire" road, but I considered them to be pragmatic rather). This however is even a little bit too friendly. Nonetheless, I'll take the gift regardless (there is no decline button anyhow, wink wink to Devs).
So, with all ingredients ready, lets cook up a nice fleet, shall we?
First we have a guardian ship class, a damage dealer:

I wanted to go kinetic in this game, but then thought: Maybe some long range missile won't hurt, either. The shadows are all kinetic from what I can see. By now, I DO have upgraded "eye of Sauron" freigthers, they tell me every little secret that "lies in the shadows". So I put one armor on the ship aswell, just to be save.
Next is my tank, an escort cruiser:

This escort has a big red flag on his hull:"I'm over here, please shoot at me!". Unfortunately for the Shadows, it also has a ton of armor on its hull aswell, so I'm afraid your kinetic weapons won't have much effect.

My first fleet looks like this. The "tank" protects the other vessels, and is the sole target the AI fires at. The "damage dealers", on the other hand, are just loaded with weapons, and in this case, one defense because I'm a little paranoid. The Shadows have the greater military power, but their ships just vaporize against my fleets. I have two fleets, and with these, they soon loose their first planet. On the screen you can also see my 10 starting planets. In the power graph in the upper corner the Korx(red), another of my neighbors, rises in power very steadily. We'll have to deal with you another turn.
Soon, my two fleets have decimated the enemy enough to take the first planet:

I move up into their territory, but the supply roads get longer. Sensor freigthers help me to spot all enemy fleets in their territory. What stops my progress is the amount of ships around Za'Ha'Doom, their homeworld. While their newer ships are all kinetic, and my fleets are ready to deal with it, on Za'Ha'Doom there are some small defense craft with lasers, mixed with kinetic ships. To "crack" this defense without too great losses, I need to built a "laser tank", which I didn't before. So 10 turns building, then another 10 turns moving them towards the enemy... tap tap tap... . In the meantime, my ships just decimate anything and besiege the planet. I didn't have suitable ships to destroy their shipyards. So after some consideration, I built what I call a "Starbase cracker" (SBC). Same "tank" setup as above, but with 24 shields, 24 point defense, 24 armor. This can take on shipyards and unupgraded starbases, while my offensive ships cover behind them and let it take the heat.
While the war is ongoing, the Korx become furious with me. Uhm, not good. The shadows are on the "left" of my empire, the Korx on the "right". They are the strongest faction in the game. Or at least they think so. Of course I am the far superior faction in this game, but I will leave them the illusion for a while. So, to avoid a war, it is time to play the "don't hurt me" card:

A wise man once said: "Diplomacy means to pet the dog until the muzzle is ready". We'll focus on the Shadows for now, and deal with the Korx later, when I've absorbed the shadow worlds into my empire. It takes its time to move up appropriate "tanks" with laser defense to the shadow world, but step by step, they fall.
Meanwhile, I keep selling worthless stuff to other nations to keep economically stable:

"This is fair".
"If you say so, buddy, I won't object you." He has just given me 2/3 of his money for a tech that won't hurt me should I ever consider to...uhm...park one of my troop transports in his orbit.
Finally, the Shadows are down to just one world. And they surrender to me, after failed peace negotiations from their side.

They still have a few useless starbases that I deconstruct, but also one precursor relic with additional 10% research. Yummy. Saves me the time to take it over when it would get pirate status. "This is what happens when you hassle with me, filthy scum!". I now have 15 worlds. The Korx are strong in missile tech, so I'll have to readjust and built new tanks for the coming war.
In retrospect, I could have been more efficient in this war timewise. There was a lot of dull waiting as I had to adjust and built proper shield tanks. This war was fought with Ion drives, so it took its time to move my fleets up. The coming war will use 2 warp drives on my ships, making them much more maneuverable. In the meantime, I had seen that the Korx are quarreling with the Earth Alliance, I so gave President Sheridan point defense techs to let them last longer.