Luggage and bags:
Nothing special here but consider a waterproof bag or maybe a bin liner to put your pack inside if you're going on a boat trip to or around Kiribati.
Clothing/Shoes/Weather Gear: Casual tropical clothing (t-shirts, short sleeves, shorts, sandals) is fine for just about any situation unless you're a business traveller and will be expected to be smart. Even then, smart dress will probably only be required by foreign companies, as I-Kiribati workers usually dress casually, even the government and airport staff.
A brimmed or peaked hat is good for the unrelenting sunshine, as are sunglasses.
Toiletries and Medical Supplies: Mosquito repellent and sun screen are the two most important and obvious things to bring, as they are not typically sold even in Tarawa. Take your own medications, especially anything prescribed. It's also worth considering taking a sterile needle kit just in case you come to harm along those lines. This will ensure your own safety and will also be welcomed by the equipment-strapped hospitals. Most commercial accommodations will provide a mosquito net but it might be worth taking your own just in case you stay somewhere that doesn't have one or has nets that are damaged or old.
Photo Equipment: Take enough film or digital memory to last you until you get back to a more developed country as there are no decent developing shops.