My favorites are the ones that are least popular with the computer players. Early game, I tend to favor beams for aesthetic reasons, but as soon as I have enough intel to see what the least common defense tech out there is, I go for the weapons that match it.

Me, I usually go for mass driver at first but that is because I was playing with the Iconian tech tree and the Scatter Blasters make good n' cheap weapons.

After I research Scatter Blasters III, I will then go with any of the weapons type with is the least popular with the computer players. Although the beam weapons I'm not too keen on since the time to get past Kinetic Streams III and Advanced Beam Weapons are huge (about the same amount of time to research Massive Scale Building).

If I'm going with beam weapons, I will trade with the Thalan.