There are many different things you can do. You could custom make a pergola or trellis then have plants going up it. Just this way you can make it the height you want though if you do this make sure that you do not have any bylaws in your area that you may need a permit of some sort.

You could do the wire thing too, but you will need to make sure it is secured properly.

Plants will not rot the would if you used wood that has been properly treated for outdoor use. It isn't actually the plants rotting the wood but water. If the water pools and there is oxygen and food (wood) bacteria will rot the wood, but if you take one of the elements away such as water then it will not rot. You do not have to have the wood that looks "green" either. Cedar is very nice and has a natural treatment in it...the resin it produces though it should have been kiln dried to keep from warping or cracking.

Look at some landscaping books or Landscaper websites that have their portfolios up to get ideas. Or if you know of a landscape designer or architect in your area call them and see if you could look at their portfolio as well and they may have some ideas or could do a design for you to the proper specs for your area and bylaws.