how do I get my iPhone contacts onto my new MacBook Pro, so that I can send iMessages from my computer, instead of my phone?
You will need to use the same iCloud device on both, and allow Messages in the cloud on both devices. On your iPhone, go to Settings > Tap your name at the top > iCloud. Make sure, both Contacts and Messages are enabled. 

Then go back to iMessage on the Mac and go through the configuration there. You may need to open iMessage preferences, then go to the iMessage tab and check most of the boxes there.