Capital ships do not require research, and the first one of them is free. If you are doing a slow start, you will have to build a capital ship factory first (which is not free), but in the fast start game you do start with a capital ship factory so you can build one right away. They do take supply points, so having one will reduce the size of the rest of your fleet, but in general the payoff is that they start picking up experience levels right away and become increasingly effective as time goes by.
As the TEC, I always start with an Akkan, and take colonization as the first ability. Then I start adding levels of targeting uplink, which happens pretty quickly as I'm knocking off the militia frigates defending the first few planets. You can go a long way in the initial colonization phase using the Akkan and a few frigates and/or corvettes as support ships.
I don't play other factions very often, but I'm guessing the same thing applies to the colonization capital ships for the Advent and Vasari.
