I've put some more thoughts into it since yesterday, so here's my take on a realistic fleet.
I feel that manned ships are incredibly inefficient; they are hardware-intensive and limited in performance. So, command of most ships would either be assumed remotely or by an "dumb" AI ("Smart" AI can't be trusted). These are good enough for a supply convoy with perhaps a pair of low-class military escort. However, neither the dubious decision making of a "dumb" AI or the delay of remote control would be any good in a battle.
For military fleets I'd imagine having a pair of large manned command ships serving as a forward RC post, supported by a variety of independent factory ships producing food and materials for the crew.
A few critical auxiliaries for any fleet would be: asteroid snatchers to bring in material, a refinery ship to process and send the various materials to other ships, a mineral assembler producing new parts and a chemical assembler producing foods and other organic compound. This chain would be critical for long term survivability of a fleet. Along with them would be a few support auxiliaries like sensor ships and maintenance drones.
The military would have a somewhat weird addition to their fleet; a telescope. Radars and sensors are alright when it come to detecting the presence of an object, but when it come to telling what that object is (and it's condition in case of an hostile ship) you want a wide-range, hi-def telescope. You could imagine having a 100 meters telescope mounted on thrusters working in tandem with sensors to identify anomalies.
I don't see the military using fighters; they're too vulnerable to lasers. Nor do I see see the use of explosive shell and missiles; again, too vulnerable to laser PD. Yet laser wouldn't be offensive weapons, they are not powerful enough to cause significant damage to armor. At best they would melt exposed electronics and vaporize or redirect micrometeorites in travel.
The way I see it most warships would sit around 50 to 150 meters, and use almost exclusively inert, magnetically accelerated ammunition and fuel. The absence of reactive compounds making them very reliable and resilient.
Keeping it short I'd say the base size of a viable fleet would be about 8-10 ships, but could go up to 60-70 and go with a roughly 50-50% ration of logistical to military for combat fleets. Trading/civilian fleet would be closer to 65% freighter, 30% logistic and 5% military.
To conclude I feel this is a pretty good base. I'd love to get into more detail on the auxiliary ships but I'd risk shrinking the scroll-bar into a singularity, so I'll leave it there. Feel free to expand on this or your own versions.