I am definitely not a great player. But here's my two cents worth. I play DA on normal mode. Sometimes I win and sometimes I lose. Although I always play the game to the (sometimes bitter

) end, I am at the point where I can recognize when I'm in trouble. As you experiment and develop your play style keep the settings as easy and as constant as possible.
In the very beginning social production is my priority, research second and military last. I work to get my planets out of the red as quickly as possible. As planets complete their structures I shift the planetary focus to military or research. I don't mess with the sliders until later phases of the game. I set espionage to 1%, production to 100% and keep taxes to have the lowest morale planet still be in the green. I have my planets build the basic structures, starports, factories, research centers, entertainment networks and markets. I flood those new colonies with markets. I leave that class four world next to mine alone until I can afford it.
I don't like the basic colony ship design. I have a few of my own designs on small and tiny hulls that I can produce quickly, they carry only 500 million people and for economy some move a little slower than the basic design. They let me spread out faster by their numbers. Depending on the board, I frequently absorb that initial 1 billion people in the first colony ship into my original population and send it off later. This will make a big difference on tax revenues and population growth, but also on morale. I may also build another space miner and four constructors (you max out the modules quickly in the early game) to put one economy base to cover as many of my initial planets as possible.
During the colony rush I concentrate research on infrastructure enhancing technologies. I try to trade as many techs that give me the upper hand as much as possible; this improves my relations with other civilizations and keeps me abreast in the arms race. I use the symptom without the cure system, for example, trading all races a defense tech for weapons I wont use, or trading toxic world colonization when I control them all (easy on the colonization techs with the evil civilizations).
As soon as the colony rush is over, well someone’s going to want what I’ve got, so it’s military build up time. My main threat has always been evil and neutral civilizations. I check the nearest military threat and how much they like me, if it doesn’t look good I drop all my spies on them to cripple their economy (econ structures) and build up my military to above their level. Research will also shift to military techs. At this point I specialize my worlds for my capitals: tech, industrial, econ, political and a world to put trade goods and galactic achievements. If I get to this point, I’ve already won. I avoid war, but if someone attacks me I absorb that civilization and change their worlds to fit my plan (it’s okay to rebuild, or demolish everything, or destroy the colony and start over). I watch the treaties and I stand ready to take advantage. I like to park constructor fleets near the mining starbases of warring civilizations, and invasion fleets near minor races.
Each turn I review every aspect of my civilization. I learned to not click away at the turn button.
Eventually all planetary improvements are researched and or my economy is strong enough to buy buildings out right on all my planets. At this point, or as necessary, I shift focus from social to military and research. I might even adjust the sliders, when I feel like doing the math to tweak it just right.
And one last thing the AI has a big weakness, military. A mobile force is always more effective than a garrisoned one. I try to control and deny access to space, this takes less ships, while the AI gets locked into controlling access to orbits, this takes more ships and is a greater expense. It is not cost effective to get “garrisoned.” Even when the enemy has hyperion defense and an orbit full of defenders I can still bring in a superior force.