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Growing up, I've always used a traditional green hose from everything like washing the car to watering the plants. I have many memories of dragging the hose around the driveway and garden. So when I moved into my apartment and then townhouse, I had a much smaller patio and opted for the coiled hose. Once I moved into a single family home, I decided to try the expandable hose (also known as pocket hose or collapsible hose) in the backyard. Each hose has their pros and cons, so you should pick a hose based your situation.
When you choosing the right hose, you'll want to take into account the durability. The more durable, the less you'll need to replace it, saving you money. If you're concerned about the weight, also consider the distance you'll need to drag the hose.
Hose Durability
Of these three types of hoses, the traditional green hose wins this hands down. I would have to purposely try to puncture a green hose for it to break. Under normal usage, I would expect a traditional hose to never break.
The coiled hose is also very durable, but the actual hose is noticeably thinner. The hose wall is thinner than a traditional hose, but also more stiff. It's a possible that a hairline crack could form over time if it gets heated up too much.
The expandable garden hose is definitely the thinnest and the elasticity could break down under the heat of the sun. Also, the constant expanding and deflating of the hose is likely to add to the wear and tear. To improve durability, I'd recommend keeping it out of direct sunlight at all times.
Hose Weight
Since the expandable garden hose has the thinnest walls, it is also the hose that weighs the least amount. The difference between an empty expandable hose and one filled with water is noticeable where the same situation is not true with traditional and coiled hoses. I'd estimate that the expandable hose is about 1/4th the weight of a traditional hose.
The coiled hose is less heavy, but because its coiled and "springy", it has an artificial weight. As you pull on a coiled hose, it has a natural tendency to try recoil back.
The traditional hose weighs the most and is sometimes a pain to navigate around the corners of the car. With added weight, durability is gained.
Hose Usage
In a traditional hose, its common for twists and kinks in the hose that cut off the flow of water. Though it's an annoyance, a simple counter-twist of the hose is all it takes to undo the kink and restart the flow of water. Depending on where the kink occurs, if its farther away from the nozzle, it may be annoying to backtrack to locate the kink. However, I find that most of the time kinks happen are causes when you're pulling the hose around a corner.
The expandable garden hose has the advantage that it never kinks. The walls of this style of hose is thin enough that it won't kink. However, that doesn't just mean you can hard pulling around sharp corner will increase the chances the the hose springs a leak. However, the best part of this is the weight. Because the hose is lighter, you can "carry" more of it with you with minimal effort.
I've never had problems with a coiled hose kinking, as the length of this hose is generally shorter. It thereby naturally reduces the chances of any kinks.
Hose Storage
The traditional hose work well in very long lengths. The hoses can then be looped around and neatly stored away on a wall mounted hose hanger. If feeling lazy, the hose can also be safely just left in the garden in direct sunlight and the durability of the traditional hose can take a beating from the sun.
The expandable garden hose also works well in long lengths, but is best to be kept away from direct sunlight when not in use. It's recommended you store this hose, but also ideal to be stored in a shady location away from direct sunlight. Leaving it on the ground in direct sunlight is will shorten the life of the expandable hose. Before you store the hose, you should also get rid of as much water as possible from the hose by squeezing the trigger of the nozzle to allow the expandable hose to contract to its original size.
The coiled hose can get long, but its more troublesome to store away. If you only need a short length, then a short coiled hose is easy to just leave hanging near the garden valve. But long lengths of coil hoses can be less "neat" to store.