Some points. Note that these DO NOT APPLY to MP games, only single-player.
It's fairly early in the game, and I keep getting missions that are patently impossible: destroy civilian structures, for example, for a race that I haven't even located yet...
You should pretty much know the galaxy before missions start coming in, unless you're playing a huge map. Very early on, build three or four scouts, give them an order to go to one of the adjoining unexplored planets, and then immediately right click their explore option so they'll go off on their own and map out the cluster for you. Good intelligence in early game is
crucial, particularly on mid-sized maps.
Defense, as already mentioned, is key. Some people try and grow way too quickly which leads to a poorly defended empire. A planet that has a decent population and decent defense (regen bay and/or hangar + 10 turrets or so positioned halfway out and covering all phaselanes and planetary surface areas) is better for you than two planets with their civilian upgrades still leeching your cash away. Get three or four planets to start at maximum and then concentrate on hardening them with turrets and a hangar/regen bay. This will hold off the invading enemy enough to get your fleet there and defend it. Further, parking your defending fleet in the middle of a cluster of turrets dramatically increases your firepower.
Finally - missions. I do my best to satisfy all the earliest "give me stuff" missions because I never know what I'm going to get as a mission the next time. If the next request does turn out to be "destroy civ buildings" on a race that's a couple hops away, the race that gives me that mission is ignored becomes my enemy. If it's "destroy ships" or "give stuff", I'll do it. On a four-player map, getting JUST ONE FRIEND is more than enough to take enormous pressure off the player, particularly if that friend is nextdoor. So - do all the first and second missions that you can, and then find a friend and stick with them. Note: if the third mission from a friend comes in and it's a "give stuff", wait until the timer has almost expired. It'll be that much longer until they give you a fourth mission, and if that one turns out to be impossible, you've got that much longer until they break up with you and become the ex-girlfriend from hell.

-- Retro