Should I use screws or masonry nails?

Don't bother with nails. You'll probably end up just ejecting the brick from
the wall, assuming the brick even survives.

If using screws, I need to put rawl plugs into the brick. What's the
best and quickest way to do this?

SDS drill with suitable bit.

If I pre-drill all the holes in the brickwork, how can I be sure to
line up the batten with the holes.

Predrill holes in all the battens first. Then put against the wall in their
final positions. Using a old smaller bit, drill through one of your
predrilled holes (above half way up the batten) into the brick to make a
mark. Remove batten. Drill and plug hole. Attach batten to hole using screw.
Use spirit level to make batten upright. Use old bit again to drill through
each predrilled hole. Remove batten again. Drill and plug each hole.
Reattach batten using screws. If you've got a steady hand or a helper, you
can skip out the steps of attaching by one screw to make the other punch
marks, but you risk misaligning the holes.

Christian.