Although carriers have a little damage in the form of drones they are very much support ships, sporting a hard-to-manage combination of neuts, smartbombs, tackle and both local and remote repair. Their primary function is repairing things, usually structures but also each other, supercapitals or even subcapitals on rare occasions. There are two primary fittings for carriers, one for general combat and one which is cap stable in triage mode for rapid repair.
An interesting feature of the carrier is the reconfiguration capability, which works thusly: When the pilot of a carrier enables reconfiguration mode, and when there are fewer than 10 ships within 5000 metres of the carrier, those ships within 5000 metres can change their fittings just as though they were docked in a station (except that T3 ships cannot switch subsystems). Reconfiguration mode is disabled by docking or jumping, so a carrier pilot must re-enable it each time. This is accomplished by right clicking the capacitor, selecting configure ship and checking the box.
The carrier's corporate hangar gives the pilot 10,000 m^3 of extra storage space, which is enough to carry as many as two spare capital modules (4000 m^3 each). Between this and the reconfiguration capability, a carrier is able to swap between its' roles while in the field. In my opinion the combat fit my alliance uses for the nidhoggur is faulty: If one swaps a neutralizer for the triage module, one can carry both a shield and an armor repper in the corporate hangar, allowing the pilot to reconfigure to full armor or shield rep as needed while still being able to triage.
Generally one will prefer to fit for combat, then reconfigure to triage when needed. Refitting from the combat to the triage fits pictured above means carrying the following unfitted modules:
1x Energized Adaptive Nano Membrane II
3x Capacitor Power Relay II
2x Cap Recharger II
1x Triage Module I (unless you take my advice and keep it fitted)
Since a fully fitted carrier will run around a billion isk, you may as well look into faction module variations. In particular, faction EANM (energized adaptive nano membrane) will give you a handy resist bonus for around 30 million each. My alliance also recommends domination or true sansha warp disruptors, but these cost 100m which I don't think is worth it. Smartbomb range can also be increased with T2 or faction variants, but this doesn't appear to increase their utility in a meaningful way.
The carrier's fuel bay holds 20,000 units of fuel, and if you carry 2 capital modules in the corporate hangars the remaining space will hold 13,333 units, which together will be enough for most ops. I can't use triage mode, but if you can it would be good to carry a fairly large number of strontium cycles, probably 10 or more. At that point it would probably only be possible to carry one capital module in the corporate hangar. If you use my idea of keeping the triage module on the combat fit, the one capital module in the corporate hangar should be a shield rep, if repping towers, or an armor rep for combat or for repairing a station -- most capitals and supercapitals are armor tanked, and station shields only need to be repped to 50% before it will go back into reinforced mode if attacked, whereas armor does not recharge and should be repped fully.
Note that only the nidhoggur and thanatos have range bonuses to both shield and armor repair. The chimera and archon will probably just carry two of the same type of repair module. They also have an energy transfer range bonus, but refitting to be cap stable would probably be easier than trying to sort out a cap chain.
I am not personally familiar with triage mode, having never trained logistics 5. Triage mode halves the cycle time of capital remote repair modules and doubles the rep amount, for a total of 4x the repping ability. It also gives a massive scan res bonus, removing the need for a sensor booster. Triage mode lasts 5 minutes, and at level 4 should burn 150 strontium per cycle. Carriers in triage mode cannot use drones, and I am unclear as to whether they can use other offensive modules such as neuts and smartbombs.
Most of a carrier's damage comes from fighters. A decently skilled carrier will do upward of 1000 dps, which would be decent for turrets but fighters are slow, and unreliable in lag. You will most likely want to use minmatar fighters as they have the highest speed.
A carrier's drone bay is generally large enough to carry around 16-20 fighters, which are 5000 m^3 each. You'll want to leave out one fighter in order to carry normal drones in addition. It's tempting to try and carry multiple flights of each damage type and category of drone in both T1 and T2 but this quickly gets ridiculous and expensive, and you rarely use them anyway. A barebones drone selection is as follows:
- Multiple flights of T2 light drones (warrior are fastest)
- At least one set of T2 sentries of each type (sentry drones have different ranges and carriers have a drone control range bonus which allows you to use even the longest-range sentries out to their falloff distance)
- Heavy shield and armor repair drones
- Heavy ECM drones (wasp EC-900 I believe)
Most boosters aren't relevant to carriers, but blue drop and exile increase local shield and armor repair amount respectively. You can see my previous post for a discussion of booster side effects; the short version is that they carry a small chance of reducing your maximum shield or armor hitpoints respectively, so you may want to consider waiting until your shield or armor is below the amount of HP the side effect would reduce you to, which is different depending on the strength of the booster.
As mentioned in my previous post, platinum capital insurance isn't worth it. Unless you're planning to suicide-triage or otherwise have a very good reason to believe you will die, I recommend basic insurance. Half a carrier's value is in fighters and modules anyway, so even platinum will only return about 50% of the value.