Ok... Selecuia will write a novel but I'll make some points
Times are in game clock time watching the replay.
1) Your scouts sat for 40+ seconds doing nothing. They should immediately begin scouting (manually directed early on if you can handle the micro).
2) Your first frigate should be the colonizer
3) Your first capital ship should be the Kortul or Egg as Vasari
4) Your capital ship completed at 1:30 and sat at your home planet until almost 5 minutes game time. This is really not good as you could have expanded to the moon and both asteroids in this time frame and been on your way to working on the Desert.
5) You built two labs before you colonized the nearby roids! Labs should wait until you initial expansion is done or if they support your initial expansion of 1-2 planets.
6) You upgraded fleet supply before you were ready to build a fleet! This reduces your income unnecessarily when you should just wait until you are ready to fleet up to make sure you get all the resources you can before that point (fleet is taxed).
7) You didn't build an actual colonizer until your capital took out the frigates at the moon (See point 2).
8) You waste time sending your fleet from moon to home world to asteroid back to moon and up to asteroid... The real approach is to scout and then determine your Expansion Path. In this case the expansion path should have been Colonizer capital ship to Moon, Colonizer Frigate to Asteroid. Colonizer capital takes moon, kills frigates to earn xp, at the same time Colonizer frigate takes asteroid and build turret next to roid (and moves to gas giant if TECH or Advent, as Vasari you should send a Scout to take neutrals!). Colonizer cap moves to roid next to moon and colonizes (earns xp). Then you move to desert next to both roids with your capital and start clearing it (The egg can take that planet just fine, kill or mostly kill planet bombers then build a turret). This part is actually very critical and plays into all the points above. Quick expansion means more early income and resources, which gives more options for fleeting or econ depending on your time.
They main theme here is quick expansion while continuously scouting. You base you next mid game moves based on this information...
Here's a quick replay against the AI solely to demonstrate minimalist early expansion (which can apply to all races). There are ways to go quicker than this, but just wanting to demonstrate the basics.
https://dl.dropboxusercontent.com/u/5790092/Temp/AutoRecord-12121042.recordreb