As in a lot of things, it depends...

Personally, I go for two quick civic labs, and then don't go back to that screen for a long time. I tend to grab as many early planets as possible and need to be able to coonize anything I find. With two, you can buff your resource gathering, colonize Ice/Volcanic, and get trade ports. Thats enough for a damn good start. Later on three more will get you into Econ-boom territory, but thats a late game scenario.

Then I move on to the military tree. By this time your scouts SHOULD have a good map of the system. You can tell who you're facing, and where they are. Are they close ? It's LRM's. Far ? Kodiaks and Carriers. Weapon tech's are nice, but they don't work for all your ships : Laser upgrades are useless for Kodiaks, carriers, and LRM's. Cannon upgrades don't help Carriers, LRM's or cobalts. Missiles don't help kodiaks, cobalts, or fighters... But Armor, Hull, and shield upgrades help EVERYONE. Drop your first upgrades here and you won't go wrong. It only takes one military lab to get rolling and at this level they are cheap. You want both armor and hull, and as long as you have 6-10 LRM's/cobalts and a cap, then the first tier upgrades will give you a slight edge.

Aftet that, it's purely situational/personal. With Carriers, I prefer to work the missile tree and go exclusively bombers, keeping flaks ( lots and lots of them ) for cover. This works well with LRM swarms, since both get the buff. My typical Lrong Range fleet has 10-15 carriers, 20 Flak, 20 LRM's, and a level 6 Marza to keep the enemy from getting to close. The extra 20-30 percent damage adds up. Ging Kodiaks ? Work the cannon tree. It's rare that you find yourself with enough cash to work multiple trees so specialization is going to happen, to a degree.

Blair, replays don't work with Alloy enabled.

Thnks for the advice guys!

hull and armor upgrades are synergistic with each other. armor is a boost to the quality level of each point of hull a ship has, which means that ships with already high base hull get comparatively bigger benefit from armor. armor also increases the value of hull repair (passive hull regen, hoshiko cruisers, and repair bays). i recommend researching hull and armor in ascending order along the tech tree (just go low to high, research whichever upgrade for hull or armor is cheapest at the moment). 

shield is on a separate path relative to hull/armor. its also not inherently efficient for TEC ships which have smaller shields than Advent or Vasari. it will give you a second simultaneous regen, and shields regen faster in combat than hulls do, but i generally don't upgrade shield when i'm playing TEC unless i've got quite a bit of extra cash. 

harder to say. i mean, it depends entirely on how well your current resource income is meeting your needs. it also depends alot on the map. you can probably increase resource income more effectively by just colonizing another planet or roid. they aren't bad upgrades by any means but i usually put them off until pretty late in the game when i get more effectively spend the extra resources on late tier research, or when i need it to off-set high fleet logistics upkeep costs. 

Generally I play the same for eco. I wait to upgrade my metal and crystal output until I have at least a 3-4/sec flow.They get pretty expensive so you need them to count. These are based off % too. If you want an early boost as tec go with the first 2 for metal as they are tier one and pretty cheap otherwise focus mainly on tradeports and colonization.Then when your creds go over 40/sec you can buy what you need fairly easy.

lol

Sins has lot's of research but you don't need all of it.  With sins it's better to go quantity>quality of ships until late game when you have your best ships (I play Vasari so I use enforcers as my best ship) and you can afford high level research.  Research that is absolutely needed is colonization research but pop cap research isn't needed until later if it's above level 1 research.  If it's a multi star map than interstellar travel is a must not an option.  Wormhole research is good but it's optional unless you rush out armies early game than you can wait for it.  Trade and resource bonus research is needed as soon as you can afford it (when I say that I mean you already have a fleet good enough to defend yourself but not good enough to attack someone else).  As for defensive research, hangers are very good a long with regeneration bays which are both in the level 1-2 research areas, so when you can afford it and once you have resource research done to an extent than get some defences up at key points.  LRM-Illuminator-Assailant research is needed ASAP even before resource research, this is because you're light frigates are next to useless and once another player has these guys your light frigates are basically raped.  Hope that helped