So, let's start with protection
Protection is the most important feature of any backpacking hat. The hat must protect your head and face from the harmful UV rays, and it has to protect your skin, and you can save a bit of money by not having to use too much suntan lotion. The hats are scored based on how much UV radiation is admitted through the fabrics.
Most backpacking hats are between UPF 30 and UPF 50. A hat with an UPF 30 blocks about 96% of UV radiation and and UPF rating of 50+ blocks 99% of the UV radiation that hits the hat. These numbers are a bit incorrect though, as if the hat has a mesh patch on the side, the UPF rating of the hat will be decreased.
|A backpacking hat in action.|
I advise you to use sunscreen with your hat even if it provides good protection. You never know where the sun might shine on your head, and it is very easy to get sunburned, especially during midday.
If your hat is not comfortable, forget it...
You are most likely going to wear the hat for hours every day, so if it is not comfortable, you are going to have a torrid time. I advise you to try out the hat before buying it just to make sure that it fits the shape of your head perfectly. You also want to check that the rim doesn't block your vision too much.
As far as colour goes, bright ones are the best, because these reflect back the light. However don't use white hats, they get dirty too easily. Find that sweet spot, and buy a hat that is not completely white. Light brown or beige would be an excellent choice.
The best hats are made of durable materials. In my opinion nylon hats are the best, they are durable, they reflect the heat back pretty well, and if they have a patch of mesh in them they are breathable and they have enough ventilation.