• Jump ship Jump ships are large, and have only minimal offensive capability. They can, however, project a hyperspace window large enough to transport an entire fleet of ships which are not themselves jump-capable. This allows the rest of the fleet to forgo hyperspace drives, and focus on speed and/or armament instead.
• Drone interceptor Fast and agile, drone interceptors are flown by remote operators to save the weight and limitations inherent in a flesh-and-blood pilot. Can be equipped with additional fuel tanks or heavy munitions, trading agility for the ability to operate over long distances or assault capital ships.
• Carrier Maintains and deploys squadrons of drone interceptors, and houses their operators. Has sufficient defences and armament to account for itself in a fight, regardless of whether fighter support is available.
• Warp transport Transports a large complement of infantry and marines. Uses the latest in short-range teleportation to rapidly deploy troops to the ground, or warp them aboard opposing ships. Effective in to boarding and capture opposing capital ships.
• Assault frigate Possesses point defence to protect against opposing fighters, but primarily armed with a variety of missiles to strike against opposing capital ships. Once enemy fighter cover is suppressed by friendly forces, missile volleys can rip through capital ship defenses with ease.

1. Armored turret. This thing doesn't really move under it's own power, aside from spinning around to aim the guns. They are placed by another ship. But they have crazy high defense and also accurate sniper cannons. Maybe they are controlled by cyber pilots on the mother ship, or maybe they are normally automated but can be taken over by a human controller if necessary.

2. Barque. This is a small, fast, agile ship. It can carry a small cargo of armored turrets, heat-seeking missiles, or big bombs. If they are not carrying missiles, their only real weaponry is gatling/strafing guns or lasers. It can land in atmosphere or dip through atmosphere to come back into space, in maneuvers most ships can't do. Holds a small crew - maybe 4 or 6. Not intended for extended use away from the mothership, as they don't have kitchens, laundry facilities, or any but the most minimal showers. Can function as a small shuttle or drop-ship by filling both the bunks and the bridge with people. Vulnerable on the ground.

3. Stealth ATV. This is a 1-2 person vehicle which has no weapons; it's extremely good at hiding and capable of functioning as an escape pod that hides survivors from hostiles or as a delivery vehicle for a spy or assassin. It is capable of returning on auto-pilot after dropping a person off, capable of operating completely on autopilot while containing a bomb or bio-weapon, and also capable of underwater operation.

4. Galleon. This is a hunter/tracker/patrol ship. A medium-sized crew can live comfortably on them, and one is a good token military presence in a friendly system. They cannot go in atmosphere or land, but they have either 2 barques or 1 barque and a cluster of stealth ATVs. They are capable of interstellar travel, and have some specialized sensor equipment that the mothership doesn't have. They can only hold a small amount of cargo, but are used for rush deliveries of vitally important stuff. Retired, de-weponized galleons function as busses or ferries, in addition to picking up small cargoes from asteroid belts and places like that. There are also science galleons which swap out most of their weapons for science equipment. They do stuff like orbit a planet and study it.

5. Mother ship. This is an armored carrier capable of carrying a ton of people and cargo between star systems. It has comfortable apartments, lots of computer power, and the bureaucracy that controls the smaller ships. Its manuverability is pretty terrible, but it can go fairly fast in a straight line. It has multiple bays where the Barques, Stealth ATVs, and Armored Turrets live when not in use. They can be used for colonization or as a military school with some changing around of equipment and personnel.

Oh, numbers... proportions in the fleet would be something like 1 Mother ship : 6 Galleon : 18 Barque : 30 Stealth : 30 Turret You wouldn't normally see 2 Mother ships in the same place unless it was a shipyard, a shore leave station or planet, or a major battle in a war. Unimportant systems would pretty much never see anything but a Galleon and it's smaller vehicles.

The task is meaningless unless I know what the enemy is :) Because that's the purpose of the fleet, to beat the enemy. If they have one measly frigate it would be a waste of resources to build any decent fleet. If they have tons of tiny light ships it would be meaningless to invest in high penetration guns (enemy has no armour). And so on, so on. There is no such thing as perfect fleet, not without the context of the task they are to serve. You always start woth the task & the obstacles the fleet will need to overcome (don't install ECM if you are fighting against legions of the Roman Empire :)).

Within the given parameters of "designing the perfect fleet" I would just build some cheap ships and use bulk of the funds to bribe the officials who decide "what the perfect fleet is", since convincing them is the goal :)

But assuming the enemy is unknown, but we know it's there I would do this:

IF THE ENEMY FLEET IS COMING TO CONQUER OUR HOMEWORLD:

Split the budget into 3 parts:

- cost effective, solid & already proven design things to defend, probably most of them stationary, focusing on ground combat siupport and orbit defence (relatively cheap and a lot of them)

- super high tech ships with high level scanners, targetting, etc in case the enemy turns out to be superior technologically and nothing else would work against them

- long range recon ships so we get at least ANY information about the enemy before they reach us

IF WE ARE TO CONQUER ANOTHER RACE (it's a simplier task, since we can always cancel the invasion if teh enemy turns out to be too strong):

- long range recon ships so we get an intel on the enemy techs and everything (these are to be bukld first and send first)

- big transport ships

- escort ships to protect the transport

- main fleet to engange the potential enemy fleet

- assault fleet to crush the enemy orbital defences and support & assist the ground forces when these take over the planet

IF IT'S A WAR FOR TERRITORY WITH ANOTHER EMPIRE (note: it's super inefficient to have only 5 types of ships in this scenario, 12+ is highly recommended):

- transporter (troops & supplies & fuel)

- main combat ship

- recon & rescue & escort ship (actually these functions should be split, it makes sense only due to 5 types restriction)

- support & hospital & repair ship (mobile base), containing a small contingent of fighters for defence and Point Defence weapons

- flagship to command the fleet (containing also fighters, long range communication systems, also should be able to function as a basic front line base (repair, hospital, minimum recreation, etc))

Optimizing fleets and ship classes without knowing the combat rules of the game and the constraints on acceptable and unacceptable ships is impossible; the survey is actually about reasonable combat rules and constraints for various conceptions of "the real world 300 years from now fighting a space war".

Two example futures:

• Reactionless drives and cheap energy sources (allowing practically unlimited range and constant intense acceleration and deceleration at the limit of passenger comfort for the whole duration of the trip, as opposed to firing rockets for a few minutes and coasting) are widely available, and as a consequence the whole solar system is colonized and well connected by fast flights, people routinely go to the Moon (a trip of a few hours) for the weekend in their family "car", and due to peace and prosperity the most advanced weapons are small lasers and railguns.
  When well-armed, slow and not stealth large fleets of malevolent aliens arrive without warning, the vastly prevalent strategy consists of suicide missions of remotely controlled and autonomous unmanned fleets of hastily repurposed inexpensive and mass-produced civilian ships: swarms of very small fighters defending and screening equally small "fire ships" carrying nukes, with the plan of detonating them as close as possible to the enemy fleets in deep space.
• The same technology, but the war is against a terrorist faction, like the current conflict between Earth and Daesh. Space stations and other enclosed habitats would be breached by bombs, railguns, maybe heavy lasers, used by rather fancy military ships of various sizes, evolved from traditional sea ship types; but most of the conflict would consist of people (terrorists, police, invasion forces, concerned citizens, etc.), not of spaceships, and certainly not spaceship fleets lasting more than a single raid. Compared to Mobile Suit Gundam, a faster time scale, less Earth and more chasing terrorists around.