In many respects, the chosen waterway will help determine the basic equipment list. Most kayaks designed for tripping or touring provide covered storage both fore and aft of the cockpit. These openings are relatively small. This limits the size and shape of the equipment that can be inserted and the volume of the dry bags (a necessity) that can be fitted. Give special consideration to the tent and sleeping bag as these are typically the bulkiest items. Important, too, is knowing how frequently it will be necessary to portage. Kayaks are not as easy to portage as canoes and will often require that the storage compartments be emptied, packed, carried, unpacked and re-stored for each portage, which is a time-consuming task. On riverways or large lakes this is less of a consideration than in areas such as the Boundary Waters where portages are frequent and the terrain difficult.
The kayak is propelled by a double-bladed paddle. Choose a lightweight one. Some are two-piece and allow changeable blade angles. Use a spray skirt. The act of paddling directs water down the paddle blade and directly into the lap. A spray skirt keeps water out of the cockpit. Use a personal flotation device. Some are designed exclusively for kayak travel and are comfortable. Dress for water temperature, not air temperature. A spill can result in hypothermia even in warm weather. Try to avoid wearing anything cotton, particularly basewear, and especially jeans. Cotton provides no warmth when wet, is heavy and dries slowly. Use instead synthetics, which dry quickly. Supplex nylon and fleece are good choices. Hats, paddling gloves, footwear, sunglasses, sunscreen, etc., should be selected as appropriate for the route. Determine the need for safety equipment-- paddle floats, navigation equipment, maps, signaling devices, spare paddles, first aid kits, tow kits, weather radio, satellite phone, bilge pump, etc.--based on experience and the difficulty of the trip. Never shortchange on safety, but remember that storage space is limited. Include what is necessary.
Camping along the wayside can be spartan or extravagant, depending upon preference. A good tent (preferably self-standing), tarp or bivy and sleeping bag are essential. A sleeping pad such as a Thermarest provides both insulation and a cushion against hard ground. Cooksets and stoves reflect eating preferences. The Trangia, which burns alcohol, is light, utterly reliable (if slow) and silent. The Zip Stove, which burns wood, pine cones, charcoal, even animal dung is a good choice where such resources are available. Other items to be included, based on need, are water purification tools, cutting implements, binoculars, warm clothing, camera, journal books, stuff sacks, bear canister, extra rope, rain gear or any of a number of other accessories that augment the safely or comfort of the trip. Before undertaking a major excursion it's always a good idea to do local trips with the selected equipment and base equipment choices on what works for your particular needs.