The ship designer is the best thing in the game since you can make your first ship very useful for the first few stages. Basically, move the aft turrets to the front. You can place three turrets simply by raising the second and third turrets a level or two above deck and concentrate firepower in the front. Mount the maximum number of barrels (or tubes in torpedos) if possible, but always pay attentention to the ship's weight. If the number turns yellow, the ship is approaching its maximum weight limit and will move a few knots slower.

Bigger guns don't necessarily mean better results, especially if you keep missing. Mount only enough guns (press CIRCLE and adjust the barrels and height) to get the ammo and damage you want to deal. Remember that the more barrels you use, the heavier the turret, and the less equipment (and armor) you can carry. When mounting guns, do not mix calibers; guns using different calibers will take up another valuable weapon space on the 1 - 7 menu. Instead, mount multiple main guns of the same (preferably the largest or most damaging) type fore and aft (aft only if you have a larger hull).

Note that the minimum parts you need for an "empty" ship hull are:

A hull
At least one engine (this means one boiler and one turbine initially)
One forward bridge
One smokestack
One radar
One sonar

If you do not have at least those items, your ship design cannot be saved, so always have extra RADAR, SONAR, FORE BRIDGES, and ENGINE parts before you start building!

Intermediate Ship Design
Once you have a few weapons and parts to play around with, you should seriously look into your design. Some quick pointers about designing for higher item-to-weight efficiency: deep deck weapons and heavy equipment (like bridges, boilers, and turbines) are greatly affected by where they are placed on a hull. Generally, the further they are from the hull's midpoint (create an imaginary line from bow to stern) the more they will weigh. For maximum effectiveness, place such heavy equipment as close to the midpoint as possible.

Similarily, where guns are placed affect what arcs they can fire on. In general, place your heaviest guns forward, and allow for at least one more mount in aft so you can perform devastating broadsides. Machineguns work best amidships, and like Starcraft missile turrets, should be mounted in triplets. Torpedoes, like most deck mounted weapons, can be mounted anywhere on a hull (even on destroyers) without any weight change.

Once Engine, Metallurgy, and Electronic tech levels are around 25, Gas Turbines and Atomic Engines will dispense with the need for smokestacks, allowing turrets and other heavy equipment to be placed closer to the ship's midpoint.

Lastly, do not mount more weapons than what is "ammunition efficient". That is to say, each weapon slot can only have a maximum of 65,000 rounds of ammo. Machineguns like the 20 to 35mm CIWS carry 10,000 rounds per gun. Assigning six of that weapon in one slot is optimal. Any more of that weapon in the same slot only uses ammunition faster with dubious effectiveness in Intercept Mode.

Research & Development
The research tree is rather lengthy, yet simple in some ways. All you need is a lot of money. Research these fields in the following order to gain new technology quickly:

Metallurgy - for bigger and better ship sizes.
Engines - a big ship that can't move is useless.
Weapons - bigger weapons mean sinking enemies faster.
Electronics - better detection allows firing at longer ranges.
Air Tech - leave planes last, when you have better ships to use them.

Be patient and replay missions several times to earn easy money. Always try to pick up parts if possible (to sell or scrap, even if you don't use them) since even if your ship is defeated, you get to keep the parts you picked up. After several replays, you'll have a very large store of weapons and equipment for your ship