If you focus on researching tech early game, and get your diplo techs ASAP, you can start trading your high level tech for cash AND the AI's planets very early, March 1 even.
The 3 Trade techs are very valuable, as are the Govt techs, entertainment techs, research techs and engine techs.
Once you get a handful of planets, get your morale high and grow your population, build econ structures and then raise your taxes, though make sure to keep approval in the yellow.
For me, and i havent played a great deal of TA, the strategy does not change.
The Terran Alliance can quickly get far above the water in comparison to the other races, partly due to their diplomatic ablities
A custom race will outperform them with ease. And on the higher difficulty levels the AI gets insane bonuses to their economy.