Well, I can give you a run down of how I play as TEC.
First off, keep the Marza!
The way I tend to expand is as follows. Buy the extractors ( i think that's what you meant when you refered to refineries. I will buy 100 crystal, sell 200 metal, and then I will buy the population upgrade for the homeworld. Also, scrap the cap ship factory after you build the marza. It's worth it.
I actually tend to get two logistics labs to start. This is because the Marza can clear all but the most heavily defended off terrans/deserts. This may sound wierd, but I like to buy at a minimum 3 colony frigs rather than 2. The slow antimatter regen rate of colony frigs is just too slow otherwise.
To support the Marza, I buy it somewhere around 10 scouts to support the Marza. That may sound wierd, but understand scouts do anti-light damage. They are VERY good against seige frigates and long range frigates. The scouts are mainly to just give early support.
Once you have three planets, that's when I get two military labs and tech for lrms. Try to place your labs so that you leave an open slot for a building at each planet. I say this because once I have the fourth planet, I make a decision.
1. I am far enough from my enemy that it makes sense to buy trade ports and set up a trade line. The sooner it's up, the sooner it will pay itself off.
2. I am fairly close to my enemy. Instead of tradeports, I invest in a mix of lrms, hoshikos, and POSSIBLY carriers. The idea here is to try to expand as quick as you can . You want planets. Getting planets is your eco boost.
Tradeports are too risk/reward to get them when your enemy is close.
As far as upgrades I definitely get, here's the list.
1. Lava/Ice Colonization as necessary ( this is the main reason I get two logistics labs early )
2. LRM tech
3. Repair bay tech: TEC Repair bays are absolutely ridiculous
4. Tier 1 of Health and Armor Upgrades. Buy these once you have a fleet maxed out on the first tier of population upgrade
5. Terran Pop Upgrade. I buy these early rather tha later. It pays itself off.
6. Modular Architecture: Extractors/Frig Facs/Cap Facs are 20%/40% cheaper. I buy this ater I get my first roid. I ALWAYS rebuild my frig factories somewhere closer to the front lines. I also build two. And then a cap factory if I'm actually going to build a second cap.
7. The tier 1 metal upgrades. I buy these once I colonize a lava.
Oh, if you see your enemy starting to spam Illuminators, switch from LRMS to kodiaks (the tier 5 heavy cruiser). If it's very early in the game, this probably isn't practical. Early on I would recommend playing a bit more defensively. Use repair bays mixed with hoshikos to hold off Illums early on. Hoshikos mixed with Kodaks can overwhelm Illums.
What's sad is if you see Guardians early on, you're probably fucked. The second an Advent player starts using repulse, TEC is done. There is no debate here. The best of the vets agree there is no counter ro repulse, so pray your friends aren't smart enough to use it right.