What's the most important thing to research?

[Nitram Draw]

There is definately no perfect research order. The key to the game is colonies so anything that helps you get more or better colonies is the way to go.
I always get Shields/PPB/PD first, even if I have to put them on an Escort. After that my order depends on the type of game I am playing.
If I'm in a large quadrant or have few opponents and I think I have a lot of time before I meet new races I go for the infrastructure, Atmospheric Converter being the goal. I personally do not capture other races and use them to colonize. I only use my own race and planet type and never research another colony type. If you plan to use all types of colonies I think a second colony type would be good early if you have the time.
If I think it is likely I'll meet some unfriendly neighbors soon then weapons, mines, ship size, etc become important.
I like to get to 100,000 research point as fast as possible so I build a lot of research facilities early on. 100,000 points lets me research almost anything in a few turns. This helps when you meet somehing unexpected.
There are so many way to play the game that I think you will never run out of styles of play. Almost any research path can win or provide a good challange.