Ozy, Civ 3 Complete contains Civ 3 Vanilla, PTW and Conquests. You don´t need a special installation of C3C. PTW is something different. All files, that are needed to run C3C are included in Civ 3 Complete, but PTW can not be started directly from Civ 3 Complete, as here the game demands a working CD in the CD player and there doesn´t exist a No-CD Patch for PTW. So to play 'only' PTW, you need a working additional CD in a CD player, but who is playing PTW today, if he can play C3C?
The GOG version of Civ 3 Complete suggests to install it in a folder for GOG games, what is no problem for me, but if you don´t like it, the folder for the installation can be changed. After the installation Civ 3 Vanilla, PTW and C3C are looking as in the screenshot below. GOG installs a launcher to start the C3C version of Civ 3 Complete, but all three exes can also be be started directly (with the special problem of the PTW exe I have tried to describe above) in the Vanilla or the expansion folders of Civ 3 and other exes can be added to those folders.
The No-CD, No Raze Patch and Antal1987 exe are working with Win 10 without any problems for me. The Quintillus editor also has no problems to work with Win 10 and Civ 3 Complete, but here another problem arises, as that editor doesn´t work with the newest version of Java. So if you have an older version of Java, that is needed to run the Quintillus editor, don´t upgrade that old version of Java. Some additional old help-programs have problems to run with Win 10, mostly cause of the 32/64 bit problem.
I have on my pc the GOG version of Civ 3 Complete, a special version of Civ 3 Complete coming with the 'Sid Meier´s Chronicles Bundle' and a German version of C3C. All can be operated under Win 10, 64 Bit,without any problems.
Edit: The GOG version doesn´t have the problem in the installation, that Bungus described, resulting from Microsoft disabling the support of SecuRom long ago. It uses the last versions of Civ 3 and its expansions, that came without the copy protection of SecuRom.