Start soon, but dont go overboard on one type. Maybe try a sample pack eg. the one from Nurture Nappies, which is a great idea, and gives you a few different types of nappies to play with until bubs arrives, and you can try out and see what fits your bub, your budget and your preferences, and your laundry situation!
I started buying early and as I could afford it, but mainly used flanny flats for the first 6 weeks. Now the tax return's come in so there's a dozen Bum Genius just been delivered! They work great for us, but there's so many options. My DP is like yours (he made the bed and our doona cover is inside out right now! seriously!!) but he's got the hang of MCNs really quickly. A few simple instructions and it's foolproof, really. Just know one thing - MCN are addictive! There should be therapists for this kind of thing!