Most boaters use a throw bag system. Throw bags are very easy to stuff and the bag makes safe storage in your kayak quite easy. When stuffing a throw bag, neatness does NOT count. Avoid the temptation to make neat loops outside the bag and transferring to the bag. This technique often results in snagged lines and short tossing distances. The best approach is to keep jamming the rope inch by inch into the bag with your fingers. When purchasing a throw bag, you want lots of room.
The next most common system is a waist bag or one that fits in your PFD pocket. These are bags you wear and are always with you. A huge advantage of this system is the rope is always ready whenever an accident takes place. This can save a great deal of time racing back to your kayak, unclip the bag, and race back to the accident scene. By the time you get back to the victim, they could be hundreds of yards downstream. Waist bags are also handy for midstream rescues where it is too difficult to reach by throwing or too great a distance from shore. One drawback of these systems is the need to make them small - typically 1/4" line and typically only 50' in length. Many boaters also carry a standard throw bag in addition to the personal throw bag system.
Coiled lines may be carried on a raft or used in a common swimming area. Be very careful when carrying in a boat to make certain it is unlikely to uncoil - this can be very dangerous. A coiled line along with a rescuer that knows how to use this system is extremely adaptable and fast. Throw ropes take forever to re-stuff and many boaters miss on their first toss (remember, practice frequently). An experienced person can gather and retoss a coiled line in a few seconds. It is real easy to toss only the amount of rope you need as well with this system. This avoids snagging the rope or bag on rocks downstream. After the initial toss of a standard throw bag, you can (and should) take advantage of the coiled throw rope technique.