Corroded copper piping
It is worth taking a step back and ask a few simple questions. Always good to understand the problem first, then the cause of the problem, then look at options, then pick an option. So let's start with the problem. You have a few spots of corrosion on your copper pipe. At this point, you don't know if there are more hidden areas of corrosion. You don't know what the cause of the corrosion is. You certainly don't know at this point what the best solution is.
So here are some thoughts on how to determine the cause of the problem.
1. The suggestion about cutting out a section of pipe and examining the inside is excellent. Once the section is cut out, you can determine if the inside is corroded, which should be fairly obvious. When my copper pipes corroded due to acid water, the insides were tuberculated (large copper flakes loose in the pipe). You could NOT tell this from the outside, all you saw were pinhole leaks, but once I removed the pipe and examined the inside, it was clear.
2. You can test the pH of your water. You can do this with litmus paper which is just a few dollars at a hardware store or a fish supply store. There is no point speculating on whether your water is acidic, basic or neutral when you can test it instantly for just a few dollars.
3. You can check the outside of the pipe for evidence of flux (flux is an acidic compound used to clean copper piping prior to soldering on fittings). Sometimes the plumber fails to wipe off the flux, and it can cause a reaction with the copper that causes corrosion over time. If there is flux remaining on the pipe, it may be possible to visibly see it on the outside.
These are three reasonable, simple and inexpensive steps to take before making a big move like deciding to replumb the entire house. Certainly you want to check the water for pH before deciding what type of pipe to use, as copper is not very good with acid water. If you do have acidic water, you can then evaluate the relative cost of putting in a neutralizer versus replacing the copper with an acid tolerant plumbing material like PEX.