Now that everyone's had time to agree that 4x's can't do naval combat & no 4xs are qualified to hold this monica of specialisation, and since Civ III is being talked about at them moment, I'll take to opportunity to say how I found Civ III to have some of the best naval aspects of any 4x I've played.
The enemy AI is still shit, but the player themselves can have a good naval experience.
If you play on a huge Civ III map and set your preference to Archipelago with maximum water & get a start which generally provides lots of islands instead of two or three big landmasses then naval supremacy can be a lot of fun in that game. It's not the most efficient way to win, but if you just want to play about with naval units then it has lots of nice options:
At the start of the game, by learning Alphabet, you can build Curraghs, small ships which help speed up exploration. They can't attack anything other than other boats & are very weak militarily even then, but are great land scouts. Excellent for getting an idea of your future plans at a very early stage.
Next up is Galleys from learning Map Making. These are just upgraded Curraghs, but they can now carry up to two units, so you can go and settle those newly found lands. The Byzantines get a Unique Unit at this stage which is itself an upgraded Galley, the Dormon, which has the Bombard ability, meaning that, for the Byzantines, naval dominance can start here if they want, being able to bombard coastal cities & weaken other boats before sending in one to sink them with a regular attack.
However, the naval game really starts to kick in during the Medieval era. The basic scout/transport ships get progressively bigger and can accommodate more people, but the Scandinavian tribe also get their Unique Unit at this point, the Berserk, the only unit in the game before the vary late Industrial age that can invade cities directly from ships without having to move onto a land tile first. Learning Navigation also enables you trade maps with other civs, allowing for a very quick map of the whole world, which is great for naval preparation. Right at the end of the Medieval era the proper attacking ships come into play with the wooden Frigate and these can bombard cities and boats, to which the English tribe get their Unique Unit at this point, the Man-o-War, which is a Frigate which also captures ships it's defeated, which are then automatically converted to new Frigates with zero upkeep cost, allowing for a huge mushrooming of your naval presence. At this point there is also Privateers you can build, slightly weaker versions of Frigates that have the advantage of being able to attack anything you like without initiating war, pirates essentially.
Halfway through the Industrial age the real meat of naval warfare starts coming into play & they come thick and fast, starting with the Destroyer, a vastly upgraded Frigate that can tear around the map extremely quickly, it's upgrade, a Battleship is just bigger and stronger but with less movement. Submarines come into play, allowing you to nestle inside enemy borders without fear of enraging them.* But one of the biggies here is the Carrier, which can carry up to four aeroplane Bomber units, allowing you to pummel anything anywhere pretty much & Bombers have the Lethal Bombardment trait, which means they can actually kill units rather than just weaken them. The other biggy at this stage is Marines, who are the Berserks that everyone can use.
From this position you can form a HUGE naval presence that can completely annihilate another island civ without any troops needing to land. The Destroyers and Battleship protect the flotillas of transported Marines and stacks of Carriers while the Bombers can sink any ships that get too close & once you're near the enemy's city you can then use all the Destroyers and Battleships to bombard the city, as well as the Bombers & then send in the Marines to clear out the remains & take the city. If you can do this to several cities at once the AI wont know which way to turn & as their stacks leave their cities to attack you, you can Bomb and Bombard them to pieces. A few land-based defending and attacking units are useful for holding the city once taken.
The modern era doesn't add much to this other than upgrades to aeroplanes & a ship and submarine that can carry missiles, including nukes etc.
*The problem with Submarines is that they contain one of the worst bugs of the entire game that was. curiously, never fixed. Because the AI isn't allowed to 'see' them, the AI will move onto a square that contains a Submarine & then automatically declare war on whoever owns the sub. Which can be a real bugger if you're running a diplomatically concerned game. Also helps explain why the game tends to turn into a mad war-carnage late game. Its one of those bugs that beggers belief as to why no-one ever fixed it, but whatcha gonna do? Avoid building subs probably & maybe invest in some Cruisers who's only real job is to spot subs with radar.
I've had a few really fun games trying to make naval power my key strategy. I'd recommend starting with a civ with the Seafaring trait, which all the above mentioned tribes have. You have to work towards it though and set your world quite carefully at the options menu & then get a good map for it.