If you're looking for traditional fencing, you first thought is probably to go with cedar wood.
Wooden fences are a classic for a good reason-they offer a good amount of privacy and look very nice. There are a number of different types of wood you can use, and some are more durable or look better than others.
Of course, you'll find that the stronger woods do cost more upfront but they also tend to require less work and last longer. A good quality wooden fence can last 20 years or so if you maintain it correctly.
A very resistant wood that holds up well to water and insects.
Handles all types of weather and remains strong after years of use.
Looks beautiful and is very strong. This can be expensive. This is due to having to pre-drill the wood because it's too dense for a nail and hammer.