I've been playing Empire since the 80's. My friend and I have played some serious games since then.
I found the Cruiser to be the main workhorse of the control and dominate sea battles - Battleships have always seemed to let you down after the long wait to build one. Subs were seldom used but effective when utilized but to a degree due to their fragility.
I used the fighters to do my sighting and their main duty in my mind was to find transports or other cruisers so I could better martial my forces. So for me fighters were extremely valuable and not to be squandered on lesser unit, unless they were about to attack a city. So the first version of empire did not have bombers,you learned to husband your fighters and primarily use them for finding and sinking transports.
Aircraft Carriers were seldom used. Destroyers were not used as much. I found a group of 8 cruisers or more to be an effective fighting force. I remember the pitched battles my friend and I had, we learned to develop like minded strategies to conquer as deviating from that script could cost you the game. The how many cruisers do you have would be asked to determine how initial neutral city conquest was going. You would really be stressed out if your opponent had a 5 cruiser lead on you as you would find yourself outgunned in critical situations. In your mind you would have an abacus way of calculating force multiplier by scouting and calculating your odds in a naval battle prior to engaging, you wanted to give yourself the best chance. On several great games I played a game could be decided early if for instance if both sides had say approx 15 cruisers per side and 1 player would win say 8 battles in a row on the same turn - So 1 player had 15 cruisers and the other say 7. Psychologically it would be difficult to remove the stigma of upcoming naval battles and the inability to project offensive strength in any one area. You would be delegated to a defensive role and would succumb to the other players dominant offensive strengths. Projecting when and where to attack is a very Sun Tzu form of warfare.
Now in the last two recent versions of Empire, the EDEE and EDCE versions I've taken the lessons I've learned from playing this game and crafted units and their performance to make for interesting battles. I've made WW2 Mods for Empire. An example of what I mean is survive ability for warships and assigning various roles for them. So with my Naval war between two capitol ships there are more likely than not be a good space barrier between ships. So you are not relying on one time epic roll of the dice for combat results, in my mod it may take several rounds of ranged fire combat before a ship sinks. This is where the survive ability comes in, after taking a pounding you can break off from an attack and sail the wounded ship back to port for repairs and for that matter as a result of conflict between two fleets you may opt to retire from extended hostilities to repair and marshall your units for another round of fighting lending to the war of attrition.
In the ww2 mod Marines can board transports, frigates and destroyers. So you would need to calculate the odds your opponent has put marines on a destroyer to make a raid on your city. I have seen the AI do just this in several games based off my AI scripts. So a single fast 4 movement space frigate can travel twice as fast as a transport - it carries only one marine not six like a transport can. So the marine unit forces a player to keep enemy frigates honest whenever they come near his city. To help counter the addition of the marine unit I also added Coastal gun fortifications to be built by seabees and engineers. The coastal gun has the range and damage of a battleship - but it's caveats are limited sighting ability (Requires airplanes or requires sighting from other units.) and no ability to move nor can it repair. But the coastal gun can help keep marauding marine transports at bay.
There are several different units I could touch upon for adding different tactics and abilities, example dedicated AA frigates, Destroyers and light Cruisers to help keep aircraft at bay.
I think that is enough to mention for the scope of this thread. But for other possible strategy and tactics consider the ww2 mod you will be able to do more and the aircraft movement won't be as restrictive as the vanilla game.