tech strat also depends on which race you are playing as - I am mainly a Vasari player (actually i pretty much only play Vasari) so I don't know the Advent's tree that well, but I have some experience in TEC's. 

For Vasari, what I like to do is max out my VIL's (Vitsurka Imperial lab) first, so I can get Highly attuned sensors (all phase jumps visible), Phase gates (extremely useful, but expensive), and Returning Armada (costs resources in v1.1 and later, but before that almost guaruntees you the victory).  Returning Armada gives you heavy cruisers, carrier cruisers, flak frigates, skirmishers, and Kanrak assailants w/o needing to research them - but you need to keep your VIL's alive.  at least 8 of them(the most technically needed).  when it comes to shields/armor/hull Vasari is one that you want to focus on shields first (they are the only ones that have missles that pass through the shield, but the missiles only have a chance to, its not guaranteed) and then evenly research hull and armor.

My TEC strat is generally to research mainly Military tree - looking for prototypes and armor/health upgrades.  they are a trade oriented civ, Advent is culture/shields, and Vasari is warfare/phase.