Ships seem totally underpowered in the beginning of the game. After researching about 30 technologies related to building ships, I can fit 1 weapon, 1 hull, 1 shield, and 1 engine on a medium craft. It does 2 beam damage, has 2 armor, 1 shield, and gets 2 movement points. If you think about it, we have jets flying around right now that are being armed with several missles (stingers), machine guns (mass drivers), and laser cannons [really] (beam weapons), and these would qualify as "tiny" class vessels.
On a tiny class vessel, you should be able to fit 1 missle launching device, 2 beam weapons, armor, a shield generator, 1 chaf, and 1 engine. A mass driver should not be able to fit on a tiny ship, because mass drivers require long barrels. In fact, a mass driver should only fit on a large or larger class ship, and it should do gobs more damage than lasers. Mass drivers should take up huge amounts of space, but they should also do huge amounts of damage, and penetrate magnetic-based shields (only kinetic shields or shields that warp space should affect mass drivers).
Also, a fleet of 2-3 small to medium sized ships with lasers and missles should be able to take on the initial fortifications you can build on a starbase (I'm talking about the very first two that give you a +7 to two different attacks).
Fleets are another issue with ships. Any government that can build interstellar ships should be capable of commanding a fleet of 10 vessels, no matter what size they are. Early on, I can't even join two constructors into a fleet. You should, by default, be able to build fleets of 5 ships. Anything past 5 ships should be based on your logistics. Instead of having each ship require 5 logistics points (or whatever) and summing them together and doing the comparison, you should say that each logistics point is another ship you can put in your fleet. Also, larger ships should allow you to join up smaller ships into the fleet and act as a command carrier. For instance, with a large ship, you would have 20 fighters, 2-3 medium ships, and 5-10 small ships as your fleet. Then, with a ship one size up from the large in the picture, you might have 2-3 copies of this structure. Each ship size up should be able to control 2-3 ships of the size smaller than it. Then, when you have a ship like a Death Star, you could have 2-3 capital ships that each control 2-3 ships one size smaller, that each control 2-3 ships one more size smaller, etc. By the time you reach the bottom, you would have something like 60-100 tiny ships and around 1000-2000 fighters. Now, I just started playing this and haven't seen any fighters, so I don't know if you even have them in this game, but this is how things normally work. The logistics points would actually be used to determine how many ships of each size smaller a particular ship can control.
Also, given the limited number of squares on the planets (and thus the limited number of factories you can build), and given the damage each ship can do, they seem over-priced (take too long to build) to be an effective tool.