Normally I use a pressure washer, but it depends on the size of the job
and how stained it is.

The one problem with cleaning just the stained areas is that those
areas may look different -- cleaner and brighter -- than the rest of
the fence. I tried spot cleaning once and the difference was too
noticeable -- I ended up pressure washing the whole thing. It really
depends on how long the fence has been up and how much weathering it
has taken.

You could tried spot cleaning and check the results after it dries. And
you may as well use your garden hose and make it part of the
experiment.

I would not use a wire brush -- stick with a good stiff plastic scrub
brush. I have a wheel brush that I picked up at an auto parts store.
One benefit is that it has a long handle.

If you go to a tool rental place, they can advise you on the proper
washer. I always go to a paint store -- what they have is geared toward
this kind of work, so there's no guessing. [If you go to a paint store
-- or even a tool rental -- plan ahead. Since this is the time of year
that homeowners start doing outside work, you may have to reserve the
pressure washer.]