Welcome and congrats on your new home!
As far as the fencing goes, I would suggest that if you replace one side, you replace all the sides to keep a clean uniform look. No need for 3 different fence types! For quick privacy, your best bet would be a 6ft dog-eared fence all the way around the property, however, some neighborhoods have height and material restrictions that might prohibit that.
If you are willing to play the waiting game you could plant a hedge. I've seen some people use closely planted arborvitaes to also create privacy screens, but I would imagine that is costly and they would eventually outgrow the space.
For the back section that runs in between the trees where it might be difficult to install a new fence, you could always install a privacy fence closer to your house and leave like a 10ft section behind the fence facing your neighbors for storage or something.
If you want a real industrial looking fence you could just paint the metal fence along the road black!
Your idea with the raised beds and trellis could work as well. You can find raised bed plans all over online or just screw some boards together and attach a frame for the trellis on the back. My only concern with this would be that in the winter whatever climbing vegetation was growing on the trellis would lose its leaves and you would have no privacy in the wintertime.
Good luck!
