The first question to ask is why you want a fence in the first place. Is it for privacy? To keep your kids and dogs contained — or to keep neighborhood kids and other dogs out? A well-constructed fence can boost property values, but a poor decision will detract from your home's value and make it harder to sell.
Yard fences for the backyard require different considerations than fence options for your front yard. Putting up a big privacy fence in front is generally frowned upon — and may even be a violation of city code or neighborhood covenant. In some subdivisions, fencing is strictly controlled by the neighborhood HOA. What kinds of fences do others in the neighborhood have already? If your idea is drastically different, you may want to reconsider that fence option.
The traditional picket fence works well in front yards and can increase the visual appeal of a house, especially if the front yard is small and undistinctive. Picket fences also provide a structural foundation for rose bushes and other flowering plants. Aluminum fencing is also an attractive option with less required maintenance. For a privacy fence, wood often works best. It doesn't really matter what type of fence you buy to keep pets and kids in your yard, just be sure to consider your animal's propensity to jump or dig. You can always consider an electric fence or other types of animal fencing if pet containment is your only goal.
This video explains why it's important to do your homework before hiring a fence installer: