Does the insurance just cover the hull or also fitting?

Does it make a price/payout difference, if I insure an unfitted ship, or do the fittings add value?

Insurance only ever covers hulls, whether it is the default insurance or purchased contracts.

Fun facts about Insurance in EVE

All ships have 40% insurance coverage by default. In addition you can insure your ship by purchasing an insurance contract, with a few details that you should pay attention to

• Insurance contracts are only valid for twelve weeks from the time of purchase.
• Insurance payout values are dynamic (effective since the release of Tyrannis).
• What this means is that after every set insurance period, an index will be created calculating the trimmed average values for all building materials that are used in the building of ships (minerals, T2 and T3 components) and when a ship is destroyed, this index will be used to calculate the full replacement value of that ship based on the materials required to build it

You receive an amount of ISK that is defined by the following:

insurance payout = (value of the ship according to the index) * (percentage of insurance coverage) * (ship type multiplyer)

The ship type multiplier is used to make some ships more expensive to lose then others (for example; a Tier 1 battleship will have a multiplier of 1, therefore receiving the full benefit of the type of insurance bought, but a Titan may have a multiplier of 0.01).

This allows insurance payouts to scale along with fluctuations in the player driven market and minimizes the risk of insurance fraud.

Fittings are completely ignored, the insurance payout is only calculated based on the ship itself. You can't insure module loss.

This is pretty much the reason why insuring a T1 frigate is usually a waste of time as the ship hull is only a tenth of the actual price of the entire ship with modules. Insurance is very useful on larger T1 hulls, though.

Another important aspect of insurance is that T2 ships get a much smaller payout than the actual price of the ship.

Your ship's fitting is completely ignored.

Also keep in mind that faction ships have very little payout! The less the tier of the ship better insurance works.

It is always good idea that you insure ship when it is giving good payout. Especially true for combat ships. And more important if you are new to game. Because you will lose ships while learning how to play. Also look at your wallet before buy a new ship. Never fly ship, that you can't afford to lose, because you will lose it sooner or later.