Old copper pipes have some problems. One is, joints were often soldered (sweated) with lead based solder. That lead leeches into the water and is a health hazard. Another is, they are really susceptible to bursting when they freeze. A third is, hard water can deteriorate them and cause green streaks and stains in the fixtures.
If this were my project, I'd want to try to strip out all the old copper, if feasible, and replace it all with pex.
2002 National Dolphin LX 6356
Workhorse W-22 chassis
Don't believe everything you think.