The first generation Neons (Dodge and Plymouth) all have head gasket issues
(bad design).  Chrysler, in their infinite wisdom of rocket scientists,
decided after the fact that the oil port to the head form the pump was too
large and provided too much oil to the top of the engine and caused a loss
of pressure in the rest of the block.  So, their fix was to make the hole in
the original head gasket smaller in order to restrict the flow.  Well, that
ultimately caused oil to leak through the head gasket to the outside world.
IMHO, they should have metered the hole with a screw-in device instead of
the gasket.  But nobody called me about it.

So, look for oil puddles near/around the left/top of the engine or down
behind the left/rear corner on top of the transmission.  Here is a good site
for it that can explain it all to you:
http://www.neons.org/

We're looking at a 95 Neon for our daughter.  Anything in particular to be
looking for?

Thanks,

Ken