No Turning Back
You cannot weld good metal to old corroded metal. So once you have started by replacing one panel it may be necessary to replace the panel adjoining it, and so on. More and more corrosion may become apparent as you strip off paint and filler. As the work escalates in this way, it becomes necessary to remove more and more of the outer trim, the chrome plated parts and suchlike. As the area receiving attention increases in proportion to the whole, the argument for painting the whole shell becomes stronger. Obviously, painting certain parts of a body is always a compromise.
So if you have reached the stage where it makes sense to paint the whole shell, do you want to go to all the trouble and expense of stripping all the exterior trim, and probably the interior, preparing the surfaces (which are so important to the final finish), painting the car, and then refitting everything, if you are going to have to do the whole exercise again when you tackle the remainder of the shell?
Clearly, this does not make sense and so you are, effectively, trapped into doing the whole job properly in one go. You may have no choice anyway as the stripped shell may be so unsound that it is unsafe.
Supplementary Work
Restoring the bodyshell properly will involve removing all the exterior trim - the bumpers, lights, door handles, soft-top (on Roadsters), glass and so on. You should be aware that refitting is not always going to be straightforward and extra costs must be budgeted for. You will need to fit new rubbers for example. You may wish to have the brightwork rechromed or replace these items as rechroming may not be practical. Items may break upon removal or be found to have worn badly. Door locks are a good example of the latter.
Even experienced restoration firms often underestimate the true cost and time involved in refitting a car. Everyone thinks that once a car is bodily rebuilt, painted and mechanically completed, that the work is very nearly done. Nothing could be further from the truth and 'refitting' is one of the most labour intensive and parts consuming stages of all. Also, the work has to be done with extra care because one slip with the screwdriver while fitting the sidelights, for example, and the resulting scratch on the pristine bodywork means a trip back to the paintshop.