I'd start with Covenants. It greatly expands on the covenant as a 'character' and provides several ready-made story hooks. I found it especially useful for first-time ArM players, as it lets them help design the setting and begin to immerse themselves in it.
After that I'd go with RoP:M. I discovered early on that I wanted to use creatures like elementals and spirits, but the core book didn't give me the information I was looking for. RoP:M covers both very well, plus the magical creature rules can be used to create fully developed familiars and the magic realm can be useful if you're going for a more high-magic campaign.
Next would be the HoH books (choose based on your PCs), then probably Mysteries Revised. I wouldn't worry about buying a tribunal book. There are several sites online with player-generated tribunals. Check Project Redcap for some good ones. redcap.andrewgronosky.us/page/overview
FM