If you are looking to contain a dog, a cheap functional option is a post and rail with wire fence. One more cheap fencing option is Chain Link. These are only a few options.
Chain Link comes in a variety of colors: Galvanized, Black, Brown, and Green. Chain Link is a very durable fence material that depending on the color can blend with your landscape to give you a clean open loop while still keeping your children and pets safe. If you have a Homeowners Association, these may not be an option.
Depending on your HOA’s guidelines you may have rules on what kinds of fence you can and can not build. Most HOA’s will allow vinyl or aluminum fencing which are not cheap but they have low or no maintenance qualities that ensure your yard will continue looking great without much effort.
One other common type of fence allowed is a wooden fence. A wooden fence is a versatile fence that can take many shapes and forms such as a semi-privacy, shadowbox, arched or scallop, cap and trim. A wooden fence may be a great; almost universal choice. A wooden fence requires more maintenance and upkeep than most fences but will last many years if properly maintained.