Well, sure I'll share with you all what I do, but I don't think my strategies would necessarily work with the huge and gigantic map sizes, just so you know. But since I don't play those sizes, I don't care.
Anyway, I have been playing around with the starting options quite a bit, but this is what I'm doing currently (I think--if the points don't add up it's 'cause I'm trying to remember this from memory): Technologists Party, Research +10, Trade +20, Influence +10 and Diplo +60. I had been playing with a lower diplo and the PQ bonus, but I didn't think it was really worth it.
Generally on the tiny and small maps I play abundant planets, and I play rare or uncommon on the large maps (don't like having to deal with all those planets).
I never go with the all or nothing colony rush. I start with setting my military to 60 and 20 and 20 for the other two. I build 1 colony ship from Sol followed immediately by a scout, followed by a constructor. As long as there are planets around, I follow the pattern of making the new colony build a colony ship followed by constructors (or scouts depending on map size--large maps I need more scouts).
My scouts go on their merry way to contact all other races asap. It's pretty essential to meet minors quickly, but I find there's usually one of them hanging around near me anyway. (Of course, it's really swell to get the Alexians really fast to get money out of them, but that's not always possible).
Generally, I start trading like crazy with anyone I meet. I try to go down the tech tree that they don't go down right away and then play round robin with the trading only stopping when nobody else has anything to offer or I have nothing new to offer. If you research weapons/photons/phasers/corvettes pretty quickly the minors will give you anything ever for corvettes, which is nice. Of course, I always start with comm theory, univ. translator and diplomacy. It's really nice to find a minor to give diplomacy to (even if you can't trade it for anything) because they'll likely build the diplo translators which you can buy off them for much cheaper than from the majors... Of course, I always try to research down the tech tree that they majors don't. I have no hard and fast rules on this, I just go with the flow. I try to get the ones that give you more trade routes fairly early (cultural trade, congolmerates...) The majors will trade quite a bit for these.
Anyway, once I get my first constructor built, I switch my production to 30 military/20 social/50 research, and I keep it there for most of the game. I usually can get at least one tasty resource as long as one's near me. If I can't get one this early then I just start a starbase in my home sector that will be used to boost production and trade income. Of course, as soon as I get trade, I also have someone start building freighters. Sometimes, if I have the tech to spare, I'll buy some freighters off the AI, which has the advantage of being able to establish the route relatively quickly. The drawback is that that freighter might have been bound for you and then you miss out on that trade route. Though, it seems the AI builds way more than they need anyway... May as well buy them.
To keep my military even with the AIs, I will also use excess tech to purchase ships from the AI. Sure, they won't give you too many, but every one you buy off them boosts you and weakens them. I don't really get how military rating works though. I think the game must count freighters because I've seen AIs with nothing but freighters with military ratings way above mine.
I really don't focus on trade goods or anything in the early game. I hope that the minors get them and trade them for them. Obviously, I never boost my social spending too high, so I use starbases to make my colonies produce very well.
I actually do research battleship and dreadnought tech fairly quickly, because I need to get to dreadnoughts to be able to build AMMs, which I use to keep my military rating high (and they work great for defense if you pay attention to the other ships coming)
I can't say that I'm always ahead of everyone in tech. There's usually one guy that's ahead of me throughout the early to mid game (usually the Torians!), but as long as I trade with everyone else, I can do alright. I like to keep the weaker majors and minors caught up with tech too, so that's where ship trading comes in pretty handy (well for the majors). And if you keep them supplied with tech, then it's easier to trade with them later when they research something you don't have.
The rest of the game just depends on my mood or what's happening. Sometimes I like being evil and just destroying all of them. One game I was really evil and bought transports from the Altarians then turned around and invaded their planet with them... Mwa ha ha ha ha. Some games I like being good. Sometimes I go for alliance victory if I'm not strong enough to win a military victory (or I get bored). Usually I culture flip quite a few (lately without even trying) and then finish off the rest with terror stars.
I guess the main focus for me is trade and research. I don't know if this has been helpful, but I'm pretty consistently ahead in tech using this strategy, so I don't think it's a fluke.
Of course, I also employ the scavenging strategies of others... Having constructors sitting around resources ready to take the resource when the other SB is destroyed. I don't really do the vulture strategy of hanging around AIs planets while they're at war waiting to swoop in with combat transports. It's not very sporting. I'll sometimes do that with the minors when they're getting beaten down, though I TRY to keep the minors around as late game trading partners as long as I can.
Sigh... I really wish I was able to play right now.