I attack all the starbases I can so I can claim the resources.

I attack miners if the opportunity arises.

I leave asteroids alone, because they'll flip once I conquer the nearby planets.

Yes, I go straight for freighters and starbases. I normally have some lightly armed, fast interceptors go after them. And I make sure I have constructors on the ready when I knock out their resources. I especially target military resources.

My focus goes to military starbases & military resources. After that it's a rush to capure some planets.
If I happen to know that the AI is short on cash, economic resources make a good target as well. That's the only case where I attack AI freighters, except if they would just happen to be in my path.
Prior to invading a planet, I also take out any morale boosters since it helps when using information warfare.

I usually stick to set of S.O.P.s

Primary Targets
anything that can contribute to their war effort and otherwise hurt me.
Military Units, Star Bases, Resources

Secondary Targets
Any Economic Structures
Star Bases, Traders, Mining Bases

Targets of Opportunity (Tertiary Targets)
Anything that wanders into my units path and doesn't detract too much time from my attack time line.



Otherwise, I try to prioritize targets on the fly which helps me assure that my attacks with be the most effective. I also try to position my forces before conflict in areas that will allow attacks to progress within five weeks of war being declared. However, it is advisable to remain flexible and carefully review each situation as it unfolds while adjusting your tactics accordingly, with one exception. Develop a fast response unit that is capable of responding to new threats as they appear insuring a small bit of tactical flexibility, This unit I usually develop as a fast one use "missile" or "interceptor" type unit that remains on standby on each of my worlds to deal with transports or other units that manage to make it past my mainline.

In case you haven't gathered it yet, resources are definitely a priority. Same for me.

On a side note, I can't remember the last time I even saw a military starbase (not the resource). Do many of you fight opponents who use several military starbases?

Amen, brothers. Those are generally the only things that I go out of my way to destroy before I begin my conquest in earnest. As Norticulus mentioned, taking out morale resources can be also be helpful, especially if you plan on taking a planet intact.

Here's a helpful hint: when you target a resource, bring along a fleet of constructors. After you destroy the enemy starbase, you and use them to your advantage in the conflict. Don't worry too much about the econ or research resource bases- the AI tends to go into 'panic mode' when it gets into a full-scale conflict, and will tank it's economy anyway, just trying to keep up. Research will slow to a crawl also, for the same reason, so there is no point in going out of your way to take them out until you are ready to claim them for your own.

That being said, more often than not I just kill everything I can, whenever I can, just for the fun of it.

Good luck. You ask the right questions; I have little doubt that soon you will be the 'sage', helping along the next generation of players.

I never bother with freighters. I play DL so there are no asteriod mining bases however I would personally turn this statement entirely on its head. Instead of thinking it's a good idea to wipe out an AI's resource mining so as to weaken the AI so that its easier to take their planets, I generally view the point of most early wars as an attempt to take over all the resources in the galaxy before I'm sufficiently strong enough to actually take out any single AI in the game.

I specifically go to war where my only intent is to take all an AI's resources and then get peace. I do this very early in the game, mostly right before the end of the colony rush, usually before I even have researched planetary invasion. Usually I'll have built my Spin Control Center and have a few cargo hulls filled with the best weapon that I have. I also have a significant advantage in diplomancy and a few attack ships that require very little weaponry to take out starbase defenses at that point in the game. I basically capture all an opponents resource mining starbases and take them over and since my military might is sufficiently better than my opponents, they will always accept the peace that I then offer.

In the case of DA you are required to wait before you can offer peace but that hardly matters much since at that stage of the game the AI generally doesn't have planetary invasion either and as long as you keep your military might advantage the AI will accept your peace offer as soon as you get a chance to make it. Of course you probably do have to wait around to actually take over the resources until the turn you are able to offer peace but otherwise I see little difference using this in DA versus DL.

Then when it comes time for "real" war your question is moot because I already own all the resources in the galaxy. However if for some reason I hadn't done this or if this was before I made owning all galactic resources such a priority, the only reason I would take out an AI's resources would be to attack his military mining resources so that his ships did not have their bonus. Note that you have to wait a turn before they lose the bonus from military resource mining.