All feeders and drinkers should be kept inside to minimise disease risk (particularly from bird flu) and to keep the food dry, as well as minimising consumption of your food by wild birds (it can get quite expensive feeding all those wild birds!)
Chickens
need to eat and drink, and we must provide them with it. We do this in
feeders and waterers. It is a good idea to keep them off the ground,
either suspended, on a block of wood or on a shelf. This is for several
reasons:
1. Bedding is not kicked in, preventing access to the feed or water and fouling it.
2. Chickens cannot poo in it.
3.
If it is kept at back height, it can prevent 'billing out' which is a
nasty habit involving using the beak to flick food out of the feeder,
wasting it.
All waterers where chicks have access should have
a thin area of water (up to around 2cm) so that the chicks cannot fall
in / climb in and drown.
Both can be made of several materials:
Plastic
I
use these, and I like being able to just look at it and tell how much
food/water is left. These are easily obtainable at pet stores (usually
sold as aviary feeders) and are fairly cheap. Some come with a place to
put a hook on the top, so that they can be suspended from the ceiling.
They will need replacing every few years, as they can crack,
particularly if dropped on a hard surface such as concrete. However,
this should not put you off.
Galvanised
These
feeders are made of galvanised metal, and are very long lasting and
durable. However, they are relatively expensive, and you cannot see the
level of food. They should not be used with Apple Cider Vinegar (ACV)
as the acetic acid has a tendency to corrode the metal, causing the
chickens to ingest sometimes dangerously large amounts of the metal.
Piglet feeders
This
may seem unlikely, but these wall-mounted feeders can work surprisingly
well. Feeders can be made of galvanised metal, or homemade versions can
be made of wood. The advantage of these is that you can simply add more
food at the top and it will drop down, it will hold a large amount of
food, as well as being low-maintenance. Not suitable for water.

A homemade wooden piglet-style feeder
Photo courtesy of Squishy0024 from BYC message board

Galvanised piglet feeder
Photo courtesy of Terri Haute
Barrel Feeders
A
homemade option for those with a large number of chickens. A plastic
barrel is taken, several holes cut around the bottom, a circular tray
larger than the base of the barrel is placed underneath the barrel. The
lid of the barrel is kept to keep chickens out of the top, making sure
it can be taken off to add more feed. Feed then comes down, as with the
plastic feeders above. These are extremely cheap or even free to make,
if you have the materials. Not suitable for water.

Photo courtesy of Edster951 from BYC message board
This feeder can be made to any size you like, although I would recommend more holes around the base than this
Troughs
I do not like troughs, even for chicks, for the following reasons:
1. They can easily be pooed in, which is not healthy
2. They can be tipped over
3. They can be rained in (although feeders and waterers should always be indoors anyway)
4. Chicks can fall in and drown
5. They take up a relatively large amount of floorspace for the amount of feed that they contain.