I use rubbing compound on stuff that's been long unprotected or obviously oxidized,
polishing compound on stuff that's less beat up looking, and paste wax afterward
to protect both the paint and the chipped and bare spots.
The car guys have a bazillion answers to this question posted on the
interwebz, and who knows more about shiny than the car guys?
3m finish restorer available at Auto zone in the paint and body section. Great stuff but remember
you have to polish after to add moisture to the paint and then wax to protect. the last 2 steps
are necessary with any rubbing compound and there is a difference between polish and wax.
polish conditions, wax protects. as far as polish i prefer McGuire's no26 or no29 one is a polish
and one is a wax both are great for step 2 & 3.
Most of what I do this on does not then get ridden in the rain, which is why god
has given us beater bikes.