I used a five gallon bucket of Thompson's Clear Waterseal to get the job done. In retrospect I should have spent a little more and gotten a slightly tinted version. At times when I was applying it I couldn't quite tell what I had covered or if I had applied enough. (Especially with wearing sunglasses.) I also wasn't sure if it would be enough but I ended up having about a gallon leftover at the end. All told it was roughly 380 feet of six foot tall fence. (Counting both sides.)
To apply it I borrowed a Wagner power sprayer from my father-in-law. (I initially tried using a roller brush but I quickly found this would have taken a long time to complete this way.) Using the sprayer I was able to do all of it in under two hours. It would have been quicker had the paint container had held more. One important thing to note however with going this route. Take the appropriate safety precautions. I wore my sunglasses for eye protection and a respirator to avoid breathing in the spray.
I still need to take a brush to a few spots that I missed or undersprayed. I also need to hand paint the edges of the fence where it meets the house. I avoided spraying too closely lest I cover the siding in sealant.