I have a '85 Regal Coupe (N/A) that I stripped and painted completely about two years ago and am now doing it again.
For a existing paint job as bad as you are describing it, yes it would be best to take it down to bare metal and the quickest way is to sand blast.
Another is to get a good electric polisher and use 80E grit sanding paper. Dewalt or Mikta but not those cheap one's at the auto parts store.
Chemical stripping is messy and the chemical's themselves are very dangerous, get some on your bare skin and you'll find out, don't ask me how I know. Sanding it down with a D/A will take forever.
Treat the bare metal afterwards with some Picklex-20 and then lay some epoxy primer (you'll need a paint gun and compressor) on the panel.
There's a good forum on auto painting called
autobodystore where you can ask away at all sorts of body and painting stuff.
The long piece of Chrome on the bottom of the door has plastic clips holding the outisde on and on each end there are bolts (mounted to the chrome) that run through the door and to remove the nuts you need to take the lower inside door panel off.
BTW
There is no cheap way to get a good looking paint job, in the end you will get what you pay for
HTH
Morbid
