I'll start by saying I still don't understand half this game, so I ignore a lot of it.

I don't claim to be a good player, just a fast one.
1) Avoid wars at all cost, they take too much time, and too many resources.
2) Automate almost all the city production through governors.
3) Only micromanage planets if really necessary.
4) Don't be afraid to just keep pressing the TURN button when nothing interesting is happening.
With no wars, and few ships outside of my planets exploring (other than a couple surveyers), I often press the turn button, and a couple seconds later I can press it again.
My 4 hour gigantic map was played without a single war (until the last 6 turns), without ever having a planet invaded or invading a planet. I really only ever had constructors moving around, and that was only to stop the Arceans who were encroaching on my borders, and getting too strong.
Unfortunately the Arceans surprised me and attacked just as I started to research Final Frontier. I had nothing but BattleAxes defending my planets and he had Overlords. Needless to say, my turns went from 5 seconds to 5 minutes as he ran arounnd destroying all my ships. I didn't bother to build new ones to defend, and just let him beat me up, knowing there was no way he could invade all my planets before 5 turns were up, and I discovered the Final Frontier. Sure enough, he never had time to invade any planets before I won, but my military was completely wiped out.
Sorry, I don't think I have a real strategy, I just don't pay much attention to details, and hit TURN a lot. I'll probably have to slow down my playing when the competition gets tougher, but I found on Intelligent they were not very much of a challenge.
Oh, one other thing, as part of my avoiding wars at all costs... I tend to be very weak as I stretch myself thin early in the game, so contrary to most people's advice, I always pay tribute in the early/mid games. I often initiate and offer tribute to people who don't like me, before they even ask, to try to increase their opinion of me. Then, as soon as I can get trade and decent engines, I start trading with all the AIs, but especially the more powerful and the ones who don't like me.
I can generally avoid wars with all the AIs, this way, so I can just race through the Tech and win without much trouble. I can also win culturally quite easily. The one thing I can't do very fast is win Militarily. Although I could, simply by culturally beating the opponents down to a couple planets and then invading, but that seems like a cheap military victory win.
I find the military ships maintenance costs are way too high to wage big wars, so I find it best to appease all the AIs to simply avoid war, and move along the Tech tree.
I'll try another Huge with higher AI next to see if I can still do it that fast. I'm going to play Huge instead of Gigantic because my computer was pretty slow for the last 25 or so turns on that Gigantic map.