I have a cat as do some of my neighbors. I had great success this year using pine cones in the beds. Fencing is fine except you have to move it everytime you want to get to your plants. I found some flexible, soft plastic fencing at Lowes and used it initially but quickly grew tired of it. One day I was picking up the abundant pine cones in the yard when the light bulb in my head turned on! Ah Ha! After that, when ever I planted some seed I would cover them with pine cones. I watched carefully every day for signs of sprouting and then moved the pine cones off to the side. One note, this won't work with just a couple of pine cones. You need to pretty much carpet your bed with them. Once the plants get big enough it no longer seems to be a problem but I keep a pile of cones handy just in case. An extra benefit is that the cat is able to patrol the garden for varmits (I don't have squirrels, yea!) but will stay out of my beds. Good luck

For situations where we are going to grow plants up the fence, and need the fence to be cheap and fast we use stucco wire. You may be able to use the fence posts you alreay have. String the stucco wire (which comes in 4' high rolls) between the posts then just add a top wood rail, or more if you want something half way down to tie plants to, and there you go! This is a quick and cheap way to fence and is much sturdier than chicken wire. It looks very nice too. PS - we also used this wire for a dog run to keep our toy dogs safe from large birds which tend to look upon them as 'hor d'eurves. LOL Because it is easier to handle than chicken wire you can use this on top of your chicken runs to keep predators out.

The real determinant should be need. Do you need the 8' height along the right side? If you don't, then 6' will suffice and you can match it to the left side fence. If you need 8', then you can run it at that height and make the transition to 6' at some other point or terminate it at the house if you don't need to connect with a 6' fence. It would look better if you make the transition from 8' to 6' height at a diagonal along the panel where the fences connect, like the following. I would consider re-working the left corner when you have the right fence installed, and getting them to match (if you use a 6' side fence. If you continue with 8', there is nothing to match.)

Pretty sure we got fencing like this in 4 foot sections....at home depot in the gardening area..(ours was taller)..but the top section was open ...had no wire ..we used it for privacy around outdoor shower....was a long time ago...and was very expensive then