Well, here's a video of a few first turns as Hazat I just made. I tried to play fast because of the 10 minute limit on Youtube, not to mention I don't really want to create half-hour long video tutorials that no one will want to watch.
http://www.youtube.com/watch?v=TVbEj_fpPdYIf I could go back and change what I did in the video, I would have moved my tank near that rebel farm that had got recaptured in order to spot the infantry. Unspotted units that you walk into 'ambush' you to receive an agility bonus (or some kind of stat bonus, I can't recall exactly which). Basically you don't want to be ambushed if you don't have to be.
More or less, you want to spend the early game rapidly expanding as fast as humanly possible. Wars this early are almost entirely irrelevant and pointless, except perhaps to establish territory over disputed planets. Don't even try to invade another homeworld at this point (and most likely, any point). I believe it's even worth risking nobles (but don't take too big a risk) in order to rapidly expand in the early game.
Don't ever attack ruins unless you are absolutely positive you have a sufficient force to take them that turn. If you don't, you'll get some angry rebels, sometimes with fleets that will launch the next turn. Likewise, never attack alien ruins with a noble. Sometimes they contain a plague bomb, and plagues can become permanent in some units. I learned that the hard way. Storing units in hospitals is the way to deal with plagues, but if the plague marker has turned to red, it's permanent.
If you're familiar with the general framework of the game, you'll know how the resource system works and the limits placed on resource city proximity. This limit is there since every tile within the 4 hex range of the resource city has its resource values calculated to add to the total value of that city's production. These stats are on the nova site, but you have to be pretty hardcore to ever manually calculate out the ideal locations. This is why farms do well in grassy areas and wells do good in water, and why some areas are trace rich and others not. Try to squish all your resource cities within 5 hexes of each other, but sometimes you might want to break this rule in order to maximize the resources you're collecting. There are only two resources that can only be harvested from resource markers, gems and exotica. Exotica is important, but nowhere near the importance of gems. Singularities really are the most crucial and limiting resource in the game, as they're required for all jump-capable ships, which will decide supremacy of the game. And gems are required to create the singularities.
Speaking of resource markers, there are ways to raze them, and I'm suggesting now that we outlaw this practice. Basically, if someone managed to raze all the gem markers on some, or most of your planets, you would be crippled for the rest of the game. It's a bug to be able to raze them in the first place, but you can when the engineer is in a stack.
Another thing I'd like to suggest is have every player vote for themselves in the first two elections, not just one. The Imperial Fleet really is absurdly overpowered early on in the game, and even 20 turns in, no one will have any remote chance of stopping it or damaging it.
Also, the combat relics are probably the most important single units in the game. You can only find these in ruins. Because of the way transports work, you can have a relic in a transport along with a fleet and gain that relic's bonus in space combat. Needless to say, save these relics for the most important times (someone declares themselves emperor, or a bitter war), because if the transport is destroyed, the relic is destroyed, and if they're captured on ground, the enemy gains control. Some players (including myself) think these should have been reduced in power a great deal or removed completely because of the advantage they give. And only one of each relic can exist in the galaxy at once. So if someone finds a certain combat relic, no one else will find it unless it's destroyed. It's just random luck to get one in the first place.
If you have any questions, please let me know. I haven't played any multiplayer games in a good 7 years or so, but I used to be obsessed with this game and tried to learn every little thing about it. I'm going to post a few of the 'secret' resource markers sometime, along with a count of the gems and exotica on each planet. Knowing what planets have gems is really important when it comes to diplomacy and weighing the relative worth of a planet. For example, Malignatius has several gem markers, which makes it one of the most important planets in the game. And to make it all the juicier, it stands only one jump away from both Istakhr and Kish.
Ok I'll stop now.