Just created a fleet with 50 logistics, Went from planet to planet, conquered every planet of 3 factions in 5 minutes. Game over. Didn't even lose one unit. All I had to do was keep building transports and sending them to rejoin the fleet. I could do this without carriers too, even just from the default design ships...no custom design whatsoever. Just building any of the large hull ships like destroyer and cruiser and putting them in a fleet together.
Also didn't really have much invested in weapons or armor or shields. spent majority of the games research in colonization tech tree. So enemies even had plenty of time to invest in other stuff before me, and I even gave enemies every resource they ever demand, whether it be tech or credits!
I think it's kind of silly how planets are captured basically instantly. I'm not even sure if military starbases are useful because I have yet to see them do anything.
So to win basically any game, start off buying colony ships with the starting credits. Colonize as many of the best worlds you can, Keep them afloat when it comes to income, and make sure to have decent production/research where applicable, then funnel all of the highest production planets into sponsoring a single shipyard, build a couple of mining rigs, up your logistics to 30-50, with maybe some minor warfare researches here and there, unlock and build a couple of transports for on standby, in the meantime research any more warfare stuff that you can, boom...go from planet to planet conquering....game over.
I used the default shipyard, and it was building the largest ships in about 3-4 turns at that point. At about 5-7 logistics per vessel, it would take about 15-25 turns to have a single full fleet that was unbeatable on its own. I actually took the time to make 3 of these fleets, and only ever used one.