The TEC are a fairly straight-forward race to start out as. Their strengths lie in their durable ships and strong economic advantages, especially in trade and planet development. You will not get the "flashy" nifty synergizing ships like the Advent, or the "doom armada" as I like to call it with the Vasari, but with the TEC you will find simpler solutions to problems, building a lot of ships and overwhelming them.
The TEC build order should also depend on what size of map you are playing. If you will only take 3-4 planets before wiping out your enemy, then I would recommend pushing for combat research. A game can be lost to the quick game TEC player if the waste their time rushing for trade ports. With that, I usually build 2 weapons labs right away, with a third coming shortly afterward.
One of the key ships to build for an early game TEC is the LRM. They are cheap, powerful, attack from range, and with enough of them can waste capitol ships and starbases alike. If you want to be aggresive build a sizeable force of them as soon as possible. I also throw a couple siege frigates in there to help bomb planets faster. Don't get carried away as they are a bit expensive, but 3-4 will help out.
The other thing to empasize is Hoshikos. The TEC is all about durablity, their weapons are not as powerful as the other two races, so in order to win you need to out last your opponent. The Hoshis can mean the difference between a fighting fleet and a fleet broken into little tiny pieces. Once you start to get a couple planets, you can research Kodiaks.
In an early game, having a fleet consisting of 2-3 Cap Ships, 40 LRMs, 15-20 Hoshis, and 25-20 Kodiaks is a powerful fleet that can take care of most enemy forces. The Kodiaks with the Hoshis to heal them will act as the shield, taking the damage and the LRMs will be the sword, dealing the killing blow.
I recommend trying something like this out either online, or in a game against an aggressive AI in quickstrike. Test it out, and try to figure out the order that works for you. As for Cap Ships, thats something I recommend you try out for yourself. Good luck, and I hope this helps.