A beautiful fence can provide a strong statement about a property by dictating the foreground element of the house when viewed from the outside, as well as the background element looking out from inside the house. Because of its strong aesthetic considerations, it is very important to consider the practical aspects of your fence: what you want it to do, whether or not it needs to be a certain level of strength, and whether or not it should impede vision enough to lend you privacy, on the same level as your visual concerns.
As always, consult with your fence dealer as to what specific materials are available for your area, but if you're looking for a wood fence, consider both picket fences and lattice fencing. Lattice fencing provides a feeling of privacy without locking the yard in due to its structure. If more privacy is desired, lattices work wonderfully with vines, which can add a sense of majesty and mystery to the yard. If you're interested in a complete feeling of privacy, talk with your fence dealer about a tall picket fence, which more effectively screens out all prying eyes from your yard.
Alternate materials can provide a different sense of ambiance than wooden fencing, including vinyl and aluminum. Vinyl can provide quite a lot of value per dollar because of how inexpensive it is to upkeep compared to wood. Many designs for vinyl fencing are "hybrid" designs that allow for complete privacy on the bottom. They also have trim that is more ornamental, allowing for a blend of practical and aesthetic concerns to influence its design. It is also possible, for example, to have a panel-style fence on the bottom with a lattice overlay on the top, allowing for a little space for ivy to grab onto while still keeping an entirely private porch.
No matter what material you use, remember that the type of fencing you use on your property is a major landscaping statement that you will send to your neighbors and guests. Therefore, be sure to give this matter the attention it deserves.