The shape of the trip
Six days, with three nights based in the Serengeti. You start with Lake Manyara on the way to the Ngorongoro highlands, cross to the central Serengeti, then come back for a night near the crater and a final morning on the crater floor.
What the extra Serengeti time buys
The difference between two and three Serengeti nights is bigger than it sounds. Two full days with no transfer mean your guide can go beyond the Seronera valley: south-west to the Moru Kopjes, out onto the eastern plains, or towards the herds if they're within reach in your month.
You can also slow down. Sit with a lion pride for an hour. Take a day where you only go out at dawn and in the late afternoon. Photographers tend to need time at a sighting more than a long list of places, and this trip gives it.
Why Lake Manyara first
Lake Manyara National Park lies at the foot of the Rift Valley escarpment, about 2 hours from Arusha, and it's on the road to the highlands anyway. Groundwater forest, a hippo pool and the lakeshore make a gentle first game drive before the bigger parks. If you'd rather start in Tarangire, that swap is easy; it adds a little driving.
Comfort and luxury versions
As written, this is a comfort-level safari: a mid-range lodge near Karatu, a mid-range tented camp in the central Serengeti, and a mid-range lodge on the highlands for the last night.
On the luxury version you stay in smaller camps and finish on the crater rim. You can also split the Serengeti nights between two areas, say two central and one in the south or north, depending on the season. That split needs the right camp in each area, and it's the main thing to settle when you plan.
When to go
The central Serengeti works all year because of its resident predators. From December to March the herds are usually on the southern plains, sometimes within a long day's reach of Seronera. From July to October they're usually far to the north. June to October brings dry weather and easier tracks.
In the long rains, roughly April and May, roads slow down and some camps close. If you're unsure which month suits you, the best time to visit Tanzania guide breaks it down.