If you bike is of an age and type which are collectible or historically significant, careful consideration should be given before doing anything to it. Choices include; Preserving the bike as is, even if not functional, simply protecting it from further degradation. Refurbishing and proper parts replacement to retain or regain functionality. Restoring to like new condition. Lastly, if the bike will be ridden upgrading to more contemporary parts may be viable. For a more detailed discussion of these options, see Jim's Velo Rendezvous Presentation , or "The 3 "Rs 'a story Jim Cunningham wrote on the subject.
Refinish only when necessary, when rust takes hold, or in cases of frame damage and then, only when all decals can be accurately replaced. On the other hand, if the bike is for casual riding and cost is a primary concern, a simpler refinish and mix of new and old components may suffice. If the intent is to ride the bike hard, or to race, then extensive upgrades to contemporary components may be in order. One consideration here is that compatibility with current stuff will help in allowing the occasional necessary interchangability with teammates or just in keeping a contemporary mechanic sane.