I like the the electric field line pictures that you find, for
instance, in Chapter 5 of Purcell's book. Near the electron,
the field points away from where it is. Farther away, the field
points away from where it would be had it not accelerated.
The transition from "near" to "far" is in a bubble that expands
at the speed of light from where the acceleration took place;
here there's a transverse field to connect the two regions. Start
by considering instantaneous accelerations, build up to oscillations
and circular motion. I think high school students could learn
something from this pictorial approach. I have put some material
on this on my web site, at http://physics.weber.edu/schroeder/mrr/MRR.html,
although this is for a more sophisticated audience.