I agree with your assessments. Beams > Mass Drivers > Missiles in terms of "most bang for your buck". So, Beams would be the quickest upgrade path... However, the AI knows this as well. There is a clear preference for the AI to research Beams weapon technologies... Sometimes eventually Mass Drivers...

In my games, the AI's prefer to research defensive tech in the same line as their offensive tech, and suddenly it becomes advantageous to research Missiles instead. (Or maybe the defensive techs also follow the same "most bang for your buck" progression)

I always base my weapons research on the defensive techs of the enemy (clearly seen in the trade window). I assume the AI does the same. I am always the last to build my own custom military fleet (prefering to buy the ships made by the #1 military civilization in the beginning of the game), so the AI has time to choose its "preferred" weapons/defensive technologies.

Consequentally... I always end up researching missiles tech, along with Shields. By the time the AI starts using Mass Drivers, it's usually not efficient for me to research a different defense line. The AI rarely researches missiles. Maybe my games don't last long enough. This is on Suicidal difficulty btw, but should hold true for Tough and up...

I can't say that theres a bias one way or another for a weapon type, as it varies per game.

In my mind, the different weapon paths come down to this:
1)Mass drivers are cheap to build, yet fairly bulky. They result in ships that are cheaper to produce but have less firepower
2)Missiles are very expensive, but very powerful by comparison to other weapons of their generation. They result in expensive ships that tend to have an edge in firepower
3)Beams are between them.

My first priority with weapons tech is always to research different weapons than my opponents, after which those factors come into effect. Some strategies benefit from the strengths of different weapons, though... a starbase centric defense will benefit from being able to churn out cheaper ships en mass, and a strategy that revolves around using a small number of powerful ships benefits from the edge missile weapons provide.

When I played games as neutral I always went with beam weapons because as pointed out above it is much cheaper to research to Doom Ray than Black Hole Gun and Black Hole Eruptor. Also it is much easier to fit beam weapons your ships than missiles (i.e., generally they are half the size with half the fire power of missiles but you can't put half a missile on your ship).
Now that I'm playing as evil rather than neutral, I have an additional reason to go with beam weapons. The evil beam weapon has more fire power(12) than the comparable evil mass(10) or evil missile(6) weapon.