Probably the most reasonably priced but nice looking fencing is the relatively new (not awfully new) white plastic fencing that is put up in sections. There is also resin privacy screening that is similar.

The most durable fencing (but expensive) is chain-link fencing.

Wood fences (post/rail, stockade, picket) are fairly durable, but they do rot. Stockade fencing sections are known for falling down after they're more than a few years old, and when one section comes down the next one will come down soon. (Of course, there is such a thing as the proverbial "fence mending".)