I did a similar trip at a similar time of year, with the addition of a Mount Kilimanjaro climb. Mine was in 2005, so the prices are well out of date, and quite possible some (or maybe all) of the travel companies booked with are no longer operating, but it was definitely a great time to be there.
I did a safari starting in Arusha, which was a
five-day, four-night safari consisting of 1 day at Lake Manyara, 3 days in Serengeti National Park and 1 day in the Ngorongoro crater. The trip also included a visit to a Maasai boma village and a visit to Olduvai gorge, though we had to pay separately for those items. Saw lots of wild life, and definitely all your must haves in abundance, and all of your nice to haves as well.
I then flew from Arusha to Stone Town, Zanzibar. I spent a couple days in Stone Town, and then some proper beach time in
Kendwa. I only had three days, and would definitely suggest more (Mount Kilimanjaro had eaten up a fair chunk of time already). Stone Town was great, the fish market in the evening was an amazing value for dinner. The beaches in Kendwa were lovely, and the water beautiful. Not busy at all.
You can read my
trip report here, which includes details of the companies I used and where I went.
Sounds like you'll have a great trip.