Protect Capital Ships needs to be equal to the value of capital ships (Crusiers and Battleships in your fleet) or capital ships recieve a penalty versus fighters (increased damage, increase critical hit chance). Example- if you have 200% PCC, you can have 2 capital ships without penalty.

Command Bridge and Communication Array need to be equal to 1/10 the total value of ships or you recieve an accuracy penalty. Example- if you have Command Bridge 200% you can have a fleet of 20 ships without penalty.

(Source- M(i)ech)

Bonus Sources

Communication Array
Frigate
Raptor (Construction 3)
Communication Array 100%

Cruiser
Space Templar (Construction 1)
Fortitude (Construction 6)
Communications Array 100%

Battleship
Emperor's Will (Sociology 8)
Communication Array 100%

Command Bridge
Battleship

Prometheus
Star of Augon (Construction 7)
Command Bridge 100%

Stellar Princess (Construction 5)
Command Bridge 120%

Thunderbird (Energy 5)
Command Bridge 20%

Emperor's Will (Sociology 8)
Command Bridge 80%

Constuction 6 and 7 make Command Bridges and Communications Arrays 50% more efficient which reduces the amount you need.

Protect Capital Ship

Corvette

Hornet
10%

Zephyr (Construction 4)
5%

Frigate

Falcon
Banshee (Energy 2)
Raptor (Construction 3)
20%

Skirmisher (Construction 4)
10%

Destroyer

Lance of Feri
Cerberus (Electronics 2)
Firebird (Construction 3)
Phoneix (Electronics 3)
40%

Guardian (Construction 1)
100%

Tonnage limits

Above 250 tonnage you get a combat penalty which increases above 300 tonnage.

Tonnage
Corvette 1
Frigate 1
Destroyer 2
Crusier 4
Battleship 5

Sample Fleets

For your starting fleets, the optimal composition is 1/10 Prometheus Battleships + 1/2 Falcon Frigates OR 1/4 Lance of Feri Destroyers.

125 Falcon Frigates
25 Prometheus Battleships

65 Lance of Feri Destroyers
24 Prometheus Battleships

Since these provide excess Command Bridge points, you can substitute other ships for the battleships.

However, rather rapidly you have access to better options at tech level 1; Guardian Destroyer 100% Protect Capital Ship and Space Templar Cruiser Communications Array 100%.

Now you want 1/10 Prometheus Battleships + 1/10 Space Templar Cruiser + 1/2 Lance of Feri Destroyers OR 2/5 Guardian Destroyer.

85 Lance of Feri Destroyers
17 Space Templar Cruiser
17 Prometheus Battleships

38 Guardian Destroyer
19 Space Templar Cruiser
19 Prometheus Battleships

Budget Council (+1 budget point)
Creative Budget Accounting (penalty for exerting budget is halved)
Deep Space Expeditions (additional expedition every other turn)
Galactic Stock Exchange (Services 25% Efficiency)
Imperial Graneries (-10% Food Consumption)
Imperial Post Office (Imperial Communication 10%)
Imperial University (10% Research Points)
Internal Revenue Service (governers -1 corruption)
Law Enforcement Agency (10 security rating)
Nuclear Weapon Conglomerate (+1 nuclear bomb per era)
Political Training School (officers +1 loyalty)
Propoganda Broadcast Tower (5 loyalty)
Secret Spies Academy (10 spies)
Stormtrooper Clonging Chambers (25% more stormtroopers)
War College (officers +1 competance)
Xeno Archeology Institute (Archeology 25%)

Budget

You start with 12 budget points (can go to 13 with project)
Going over budget costs
300
600
900
1,400
1,900
2,400
3,200
4,000
4,800
5,600
6,400
7,200
8,000
8,800
9,600
10,400
11,200
12,000
12,800
13,600
14,400
15,200
16,000
16,800
17,600

Development Level

2 for minor races, 5 for major
3 for empire at the start
+.25 (Consturction 8)(Energy 9)(Electronics 9)(Biochemistry 10)

Imperial Communicaion Range

Base (Administration)
80/120/140/160

10% Imperial Post office
-20% less than 60% electricity
10% edict Couriers
10% long range administration
10% (Electronics 5)
30% (Sociology 6)
5% (Sociology 11)
10% Cancelists (political faction)
25% hydrogen

Max 110% bonus or 336 parsecs

Communication Range
1 10% loyalty
2 3% loyalty -8% taxes
3 -16% taxes
4 -24% taxes
5 -32% taxes

Research

3% character creation option
3% edict education
-30/0/10/20% budget
5% (Electronics 2)
2% (Electronics 7)
5% (Electronics 12)
3% (Bio-Chemistry 1)
5% (Biochemistry 4)
12% (Sociology general bonus)
5% (Sociology 2)
1% (Sociology 10)

64% max bonus

Construction (1% industry output)
1 SHIP SHIP
1 20% heavier versus tractor beam 25% resist PD
2 10% factory 10% mine
2 Turret 1 (5% damage)
3 5% HP 5% HP with Tritanium SHIP
3 SHIP
4 2% output per level of electronics (max 20%) SHIP
4 SHIP SHIP
5 Turret 2 (10% damage)
5 5% ground combat
5 SHIP
6 SHIP Communication array 50% more efficient
6 5 electricity lava planet 4% damage
6 Turret 3 (15% damage)
7 SHIP Command Bridge 50% more efficient
7 5% HP
8 +.25 planetary development
8 Turret 4 (20% damage)
9 10% archeology
9 10% heavier versus tractor beam 30% resist PD
10 8% ground combat
10 2% damage
11 double prestiege of imperial palace
11 10% factories
12 Turret 5 (25% damage)

Energy (5% damage 10% stronger tractor beam 3 nuclear power)
1
2 30% PD
2 Shields 1 (0/1/1/2/2) SHIP
3 Powergrid 1 (5% damage)
3 20 nuclear power
4 Energy techs 5% cheaper
5 SHIP
5 Shields 2 (1/1/2/2/3) 25% chance to halve enemy shields
6 10% mines
6 Shields 3 (1/1/2/3/4) 10% HP
7 10% refining 5% HP with Braxium
7 Solar Energy (planets produce electricity)
7 Powergrid 2 (10% damage)
8 Energy techs 5% cheaper Powergrid 3 (15% gamage)
9 +.25 planetary development 10 nuclear power
9 30 nuclear power
10 Shields 4 (1/2/3/3/5)
10 Powergrid 4 (20% damage)
11 20% PD
11 5% ground combat 10% imperial bodyguard
11 3 spying
12 Shields 5 (1/2/3/4/6)
12 Powergrid 5 (25% damage)

Electronics (1% accuracy)
1 Scanners 1 (5% accuracy)
2 5% PD 3% damage
2 5% research 5% ground combat
2 SHIP
3 SHIP +1 spying per construction
3 halve command bridge/communications array penalty
4 -1 corruption (governer) Cities hold 10% more people
4 +1 competance (military)
5 Scanners 2 (10%)
5 5 happiness 10% imperial bodyguard
5 10% communication range
6 Cities hold 10% more people 3% accuracy
6 fighter damage 30% PD 10%
7 +1 loyalty (military) 2% research
8 10% farm
8 10% factory
8 10% mine
9 +.25 planetary development
10 Cities hold 10% more people
11 fighter damage 30% 1 spying
11 Scanners 3 (15%)
12 5% research

Bio-Chemistry (5% HP 3% ground combat)
1 10% combat 3% research
1 Thruster 1 (20% heavier vs tractor beam) Armor 1 (0/1/1/2/2)
2 Cities hold 10% more people
2 5% HP
2 50% farms
3 Armor 2 (1/1/2/2/3)
3 5% HP 10% ion resistance
3 +1 loyalty
4 5% research 10% grounf combat
4 -5% food consumption 1 happiness
5 Thruster 2 (40%)
5 Completed a turn faster Repair (40%) Construction (30%)
6 Thruster 3 (60%) fighter damage 20%
6 5% HP Armor 3 (1/1/2/3/4)
7 5% HP
7 10% ground combat 10% imperial bodyguards
8 10% refining
8 10% HP
9 fighter damage 25% 3% ground combat
9 Thruster 4 (80%)
10 +.25 planetary development
10 Armor 4 (1/2/3/3/5)
11 Thruster 5 (100%)
11 fighter damage 50%
12 15% HP
12 Armor 5 (1/2/3/4/6)

Sociology (1% research and happiness per level)
1 10 luxery 2 per electronic level 15 security
1 higher diplomatic audience event
2 3 spying
2 5% research +1 competance (50% chance)
3 5 happiness
3 double influence over minor races
4 10% PD 3% ground combat
4 12% ground combat 20% imperial bodyguard
5 20 luxury 50% foodtasters
5 3 accuracy
6 5 happiness
6 30% communication range half communication range tax penalty
7 10 morale
7 -1 corruption (courtier) 5% cheaper capital ships
8 SHIP 15 morale
9 double development
9 30% archeology
10 1% research 10% archeology
10 3% accuracy 5% PD
11 3% tax 5% communication range
11 15 morale
12 25 spying

Imperial Warships

Corvette

Hornet
4 laser beam (6-12)
2 PD
HP 157
---
10% cheaper
10% Protect Capital Ships

Zephyr (Construction 4)
4 ion beams (6-12)
25% damage to biohulls
2 PD
HP 150 (Armor 1)
---
5% Protect Capital Ship
Immune to Tractor Beam
-30% enemy accuracy

Frigate

Falcon
6 Laser Beam (6-12)
2 PD
HP 200 (Armor 2 Shield 1)
20% vs Corvettes
Protect Capital Ships 20%

Banshee (Energy 2)
6 Ion Beam (6-12)
25% versus biohulls
2 PD
HP 200 (Armor 2 Shield 1)
75% bypass shields
Protect Capital Ships 20%

Raptor (Construction 3)
6 Laser Beam (6-12)
2 PD
HP 200 (Armor 2 Shield 1)
Protect Capital Ships 20%
Communication Array 100%

Skirmisher (Construction 4)
6 Laser Beam (6-12)
2 PD
HP 200 (Armor 2 Shield 1)
Protect Capital Ships 10%
Tractor beam 5k tons
Immune to Tractor Beam

Destroyer

Lance of Feri
6 Twin Laser Beam (20-40)
5 PD
HP 400 (Armor 4 Shield 2)
Double Critical Chance
Protect Capital Ships 40%

Guardian (Construction 1)
6 Twin Laser Beam (20-40)
5 PD
HP 300 (Armor 4 Shield 3)
Protect Capital Ships 100%

Cerberus (Electronics 2)
6 Twin Laser Beam (20-40)
5 PD
HP 400 (Armor 4 Shield 2)
25% chance to bypass enemy armor
Protect Capital Ships 40%

Firebird (Construction 3)
6 Twin Laser Beam (20-40)
5 PD
HP 300 (Armor 4 Shield 3)
2 fighters
20% cheaper with Tritium
Protect Capital Ships 40%

Phoneix (Electronics 3)
6 Twin Laser Beam (20-40)
5 PD
HP 300 (Armor 4 Shield 3)
Protect Capital Ships 40%
50% will be repaired instead of scrapped when destroyed

Cruiser (capital ship)

Ariel
4 Laser Cannon (40-60)
12 PD
HP 420 (Armor 7 Shield 6)
4 fighters
10% Accuracy
+1 bonus to 4 friendly ships

Space Templar (Construction 1)
4 Laser Cannon (40-60)
12 PD
HP 700 (Armor 5 Shield 4)
4 fighters
Communication Array 100%

Stellar Spirit (Construction 4)
4 Plasma Emitters (25-35)
5% versus capital
12 PD
HP 700 (Armor 5 Shield 4)
20 fighters

Fortitude (Construction 6)
4 Laser Cannon (40-60)
12 PD
HP 700 (Armor 5 Shield 4)
10 fighters
Tractor Beam 10k tons
Communications Array 100%

Battleship (capital ship)

Prometheus
6 laser cannon (30-60)
10 PD
HP 1000 (Armor 9)
Immune Tractor Beam
Command Bridge 100%
+1 bonus to 8 friendly ships
+2 bonus to 4 friendly ships

Stellar Princess (Construction 5)
6 laser cannon (30-60)
10 PD
HP 1000 (Armor 8 Shield 5)
Command Bridge 120%
+1 bonus to 25 friendly ships

Thunderbird (Energy 5)
6 ion cannon (30-60)
25% vs biohulls
10 PD
HP 500 (Armor 4 Shield 20)
20% bypass enemy shields
immune to bypass
Command Bridge 20%
+1 bonus to 4 friendly ships

Star of Augon (Construction 7)
6 plasma (40-50)
5% vs capital
10 PD
HP 1000 (Armor 8 Shield 5)
10% bypass enemy shields
Tractor Beam 20k tons
Command Bridge 100%
+2 bonus to 5 friendly ships
+3 bonus to 5 friendly ships

Emperor's Will (Sociology 8)
6 laser cannon (30-60)
10 PD
HP 1000 (Armor 8 Shield 5)
double cost
immune to tractor beam
Command Bridge 80%
Communication Array 100%
+1 bonus to 50 friendly ships

Enemies of the Empire

Civilized Aliens

Watcher
4 laser beam (6-12)
2 PD
HP 150 ceramic (armor 1)
Protect Capital Ship 10%

Serpent
6 laser beam (6-12)
2 PD
HP 200 (armor 2 shield 1)
Protect Capital Ship 20%
Tractor Beam (2k tons)

Ceres
6 Twin laser beam (20-40)
5 PD
HP 300 (armor 4 shield 3)
Protect Capital Ships 40%

Hydra
4 ion cannon (30-60)
25% vs biohulls
12 PD
HP 700 (armor 5 shield 4)
2 fighters
Communications array 100%

Saladin
6 laser cannon (30-60)
10 PD
HP 1000 (armor 8 shield 5)
4 fighters
Command Bridge 100%
Communications Array 100%
+1 bonus to 8 friendly ships

Rebel

Rebel Corvette
Rebel Frigate
Rebel Destroyer
Rebel Crusier
Rebel Mothership

Pirate

Pirate Frigate
6 laser beam (6-12)
2 PD
HP 200 (Armor 2 Shield 1)
2 fighters
Protect Capital Ship 20%
Tractor Beam 1k ton
75% resistance to planetary defenses

Pirate Crusier
4 laser cannon (30-60)
12 PD
HP 700 (Armor 5 Shield 4)
2 heavy fighters
6 fighters
Tractor Beam 5k ton
Command Bridge 25%
Communications Array 25%
+1 bonus to 8 friendly ships
75% resistance to planetary defenses

Bio (Hive and Parasite)

Bio Corevette

Bio Frigate

Bio Destroyer

Bio Crusier

Bio Battleship

Annihilator (xeon hull)

Annihilator Corvette

Annihilator Destroyer

Annihilator Crusier