Disclaimer: It's been a decade since I was there, maybe some things have changed (surely some have), but...
We went around the same time of year (late May into early June). We took several ferries, though we also had rental cars in places. For ferry info, I used these two sites:
I used these as a starting point, then for actual bookings, I went to the actual company's website (just as I would when researching then buying flights).
As to your question about booking ahead versus just 'winging it', I would say that depends on if you are just walking on, or taking a vehicle. I doubt ferries sell out in advance for foot traffic, but I'm sure they do for vehicles.
May is a good time to go, with relatively few crowds (except in Split and Dubrovnik, I think the cruise ships bring crowds year-round now). Be careful about ferry schedules: IME they were highly seasonal...some lines only run during "high season" then either only run a day or two per week, or shut down entirely. When we went, "high season" started in late June and ran through end of August. Before/after then, frequencies were totally different.
Hope that helps.