The title says it all, but I'd like to begin with a disclaimer: I have some idea what I'm doing. I'm a veteran of Supreme Commander, so I'm familiar with the idea of keeping up the flow of units whilst scouting and expanding your territory to acquire Moar Resources. I'm also familiar with the idea that, in general, static defenses are wasteful because the enemy can: 1). Go around them, and 2). They can't go elsewhere. There are always exceptions, of course: pirate raids, for example, or choke points, or areas that the enemy can't otherwise go around. To be honest, I prefer repair bays over most static defenses because they can actually allow a planet to serve as a staging area, and they can allow your fleet to defend the planet more easily.
Generally, I play as the TEC, because it's straightforward, but I'm fairly certain I don't play it well. I loathe the Advent (they seem like easy mode to me), and I'm eyeing the Vasari, wondering if I can do anything with them (I read a post recently about nine Antorak Marauders > nine Marza Dreadnoughts, and it intrigued me).
I'll begin with what I think I know (TEC):
1). Hoshikos + well-armored units = win
2). Get trade ports ASAP to roll in the money
3). Make sure you create "fleets" so that your Hoshis and missile ships stay together.
4). Missile frigates die quickly
5). Deploy Dunovs in pairs, if possible.
6). Begin with an Akkan Battlecruiser to colonize on multiple fronts (Moar colonies = Moar cash)
7). Use Flak Burst against lots of fighters; Flak Burst is generally > Gauss Rail Gun.
...that's about the size of it. Some of it is probably wrong, though. Now, I'd like to pose a series of questions for you.
A). What is the general build order for starters? What structures and ships should I get first? Should I go for the old, "Get first capital ship, sell factory?" approach? What is a good capital ship to start with for TEC and Vasari?
. What should TEC players emphasize in research and deployment? Moar Hoshis? Moar missile frigates? Moar Kodiaks? Should TEC focus on civilian or military research, and if so, what should that research be (what works, in other words, and what is a waste of resources).
C). Same goes for Vasari: what should they emphasize? Should they go for more military research, or civilian research, and if so, what?
D). TEC Economics: what is most important? Trade stations? Orbital refineries? Moar colonies + Population increase research? Increased income rate on mining facilities?
E). Vasari Economics: what should I go for? I have no idea where to start.
There we go. Any suggestions?
EDIT: We've got some fantastic suggestions thus far (thank you very much, Kruppe), but the following questions are still unanswered:
1). Vasari power units (and by this I mean, units that play a pivotal role in strategic play):
-ANSWER: Jarrasul Evacuator, or Flying Space Egg
-ANSWER: The Antorak Marauder is lame until level 6, unless you really like running and disabling key vessels
-ANSWER: The Skirantra Carrier has a very nice stackable AoE heal -- use in pairs (like the Dunov!)
-ANSWER: The Desolator can flatten a planet faster than anything.
2). TEC power units (besides the Marza)
3). Intermediate Vasari economic steps
4). Intermediate TEC economic stepping stones -- the important ones
5). Important Vasari military technologies besides the aforementioned phase gates and the phase missiles?
-ANSWER: In Entrenchment, The Kostura will be King 
6). Is the Kortul Devastator any good?
-ANSWER: As a tank? Not as good as the Kol, but it can really kick out the DPS with Power Surge
