Trade Port strategy

It depends on how many and what sort of planets you have. In the end, if you'll be fighting a long war of attrition, you'll definitely want to fill out all leftover slots with trade ports (or, rarely, refineries).

When I get trade in the first place I try to build my starting trade chain using only the default logistics slots, without upgrading. After that I get the (cheapest) logistics upgrade on asteroids, which gives me 2 more slots for trade cheaply. Then I can upgrade a single full-size planet twice, giving me +1 then +2 logistics: after doing that I upgrade my only remaining planets, Deserts, twice again, giving me +1 and then +2 again.

Yes, it's expensive, but you should be scouting your enemy almost continuously to make sure that you'll be able to at least fight them off (build enough ships) if they attack - if you have the spare funds to build trade ports while your fleet is strong enough, go for it!

(Of course if you're in that situation you could also consider attacking if it could give you a significant advantage or a quick win, but usually I'd prefer to max out trade first)

I would say in general it depends on the map set up...if your opponent has more "potential" than you such as more planets, or better planets like deserts/terrans then you need to go on the offensive fast...even if the odds aren't in your favor, they can only get worse if your opponent has better opportunities and potential...

If you are in a highly favorable position, it general is to your benefit to drag the game on and maximize your economic edge...while slow, it is a safer strategy with less risk....just don't let a rush catch you off guard...

So should you fill those expensive logistics?  It depends on whether you need to go offensive fast or not, and that is determined by how good your map position is (team dynamics of course complicate things)...

Wrath's suggestion is a really good one...try to use that free logistics slot on each planet for trade, and upgrade the asteroids first (since the upgrade will take you from 1 to 3 structures)...

It should be also important to note that TEC has a huge economic advantage over all the other races. So economy plays a huge role for them. Especially when it gets to late game when clearly Advant and Vasari have a military tech advantage so that leaves you using eco to spam out your opponents.

The sooner you implement the economic and resource improvements, the longer they have to return their costs.  The larger your production and economy, the greater the returns.

The issue is that at the game start, every economic investment you make takes away from fleet building...not enough fleet and then it doesn't matter how large your economy "would have been" with all the investments you made.

What it comes down too is how well you can manage and preserve your fleets--what's left over can go into research and economy.  Then you have to decide is it research for economy or other things you need. It then comes back to, "What do you need to keep your fleet alive and sufficiently strong?".

The overall point of a large economy is to fund large and effective fleet actions.

I wouldn't say "huge" - it's significant but not overpowering, except in long or large games where Pervasive is an option. That said, they definitely do have to depend on ship spam much more than the other races.