I'm just trying to figure out what all the strengths and weaknesses of the races both in regards to combat and economy.

By no means an exhaustive list and I'd definitely like suggestions for the strengths and weaknesses of the races and the ways to use them and abuse them.

Vasari
-Generally are the more militaristic oriented of the three
-They get missile frigates a lot earlier and their missile frigates are actually cheaper than their light frigates (less credits, less metal, small crystal cost)
-They get their crystal and metal production increase techs combined together so they're a lot more cost effective

TEC
-Generally are the more economy oriented of the three
-Get a LOT of armor increases to their ships
-Get a long line of upgrades that increases the healing from repair stations
--Those two combined maybe a good strategy would be maxing out the survivability of your ships and retreating them to be healed by a repair planet?

Advent
-Generally are the more culture oriented of the three
-Get carrier cruisers VERY early (tier 2 military)
-Seem to be very fighter oriented when it comes to combat