In my humble opinion, Wagner sprayers work really well....as long as your using them as a boat anchor, for any other purpose, they're frustrating pieces of junk. I'm with DH on this, rent an airless and discuss with your rental business what tip you need to use. I'm a little rusty on airless sprayers as I don't typically do that kind of work anymore. I think what you need is a .021 tip for latex work (don't quote me on that one) Make sure that the unit you rent has a reversable cleaning tip as clogs in airless can be a real time waster. Also discuss what they require you to do for cleaning after you use it. Most places want you to fill the lines with mineral spirits.
To calculate how much paint you'll use, you should measure the hight and width of your fence and calculate the square footage as though it were a solid wall. Read the label on the paint your useing, under coverage it should give you the number of square footage per gallon, most cover about 350 to 400 square feet. Figure you'll get 25 to 50 square feet less because of a breeze and for overspray and bounce-back.
Here's a little advice on if your making the right move. Most contractors do what is called "Back brushing" and "Back rolling". One person sprays while 2 or 3 other people go behind and brush or roll over the paint. The reason for this is because the paint gets a better bond than if you just spray alone. Even though you have primed the surface, there is a texure to your fence that the sprayed on paint will just form a film over and not really bond to your primer. Back brushing and rolling works the paint into the surface. This is one reason I no longer do this type of work. I find that, in a one man operation, spray just isn't the way to go if you want it to last. I'd just roll up my sleeves and use combination of a brush and roller.