A MacBook is a independent computing device, like the Mac Pro. Each has its own independent iTunes library. An iPhone or iPad (starting with iOS 5) can be an independent computing device, but it can also be a dependent device that syncs to a computer's library through iTunes.
For syncing music, Apple's solution is iTunes Match. The service costs $25 per year. In your case, you would use your Mac Pro (which I assume has all of your songs in its local library) to "match" or upload your songs (including playlists) into your iCloud Music Library. Let your Mac Pro finish first. You then associate your MacBook, iPhone, and iPad to that iCloud Music Library, setting up the iPhone and iPad to be independent computing devices that sync to iCloud instead of directly to a Mac. All four can access the same iCloud Music Library, to stream songs, use its playlists, or download songs to local storage. Each one can make changes to the iCloud Music Library, and those changes are seen by the others.
On the Mac Pro, you should keep a local copy of all of your song files (you don't have to, but you should). If you buy a song on the iPhone or iPad or MacBook, that song is added to your iCloud Music Library. At the next opportunity, download that song on the Mac Pro (or use the setting in iTunes to automatically download purchases). On the MacBook and iOS devices, only keep (download) a portion of your full music library from your iCloud Music Library, or just play your songs from iCloud. A secondary benefit of iTunes Match is, for songs that "match," you can download the 256 kbps AAC file that the iTunes Store sells, which may be of higher sound quality than your original file. These song files do not have DRM (copy protection), so you can "upgrade" ALL of your inferior song files (that match) and keep them, even if you later decide to cancel your iTunes Match annual subscription.
For other media types like movies and TV shows that are purchases from iTunes Store, you can already stream or download them on computers or devices associated with your Apple ID.
