First, welcome to SingleDivers.com, I think you'll find a fun group of dedicated divers here, who will be happy to give you their 2 psi of advice.
You've picked one of my favorite spots in the world, Raja Ampat, to dive, although I admit the bucket is still full of places I haven't been. I will be making my third trip to Raja Ampat/Indonesia for the Oct. 2018 SD trip. My first trip, Oct. 2008, was land based in southern Raja Ampat for 12 days, I saw 2 liveaboards during my stay. I returned in Feb/Mar 2013, on 2 different boats. There were 10 liveaboards in the same area on the same day!!! Before the 2013 trip I spent days searching different liveaboards, for accommodations, schedule, availability, price, etc., before I could put together an itinerary. The biggest problem is availability, most are chartered/booked as much as 2 years in advance, primarily to groups [ex.-a dive club from Belgium 9, a pair of Dr. couples from Spain, my daughter & I]. I agree with you concerning the length of stay, at least 10 days, there's so much to see. Suggestion, become more of a 'hard core diver', you don't know what you'll miss if you decide to skip a dive [wobbegong shark, manta, etc], and absolutely make all the night dives offered [epaulette walking shark, etc].
Besides the all of the diversity of fish, corals and pelagics, there's one thing which bring these all together, the combination of currents of the Pacific & Indian Oceans. The variety of the different types of dive sites; walls, pinnacles, muck, present different challenges/techniques for divers. What do you do when, you see your bubbles not going up on your safety stop??? What fin technique do you use when muck diving??? Are you comfortable diving from a zodiac type dighy??
There are probably at least 20 boats which schedule cruises to Raja Ampat, some are affiliated with some of the world wide operations - Siren, Aggressor - most are independently owned - some are motor yachts - most are - phinisi-s - a motorized sailing yacht [will 'show' their sails once during the cruise]. Cost will probably range from $3,000-$8,000 [but be prepared to be priced/pay in Euros] for a 10-12 day cruise. You can do a search for 'Raja Ampat liveaboards' and numerous 'agency' websites, that provide information on a number of boats and booking services. As I've said you can spend days [dazed] at a computer screen trying to find the one that appears to suit your needs, only to discover it's already 'full'.
You've made the decision to dive, what some would declare as, 'the worlds best diving', you might as well go all the way, and go on a great boat, Damai II, October 2018. I'll be on the cruise, and I'm planning on making some other stops in Indonesia, both before and after. If you or anyone else is interested, you can join me.