With 7 days I will advice to do amboseli,lake Nakuru and Masai mara. Out of my own personal experience you will be able to spot the big five as we did.
I will recommend you book with local tour operator because they have better deals.
Enjoy your holiday.
The safari we did started and ended in Nairobi,which we booked through Mombasa based company. Actually to me i was upto better deal and good service with the help of tripadvisor members. So with that it does not make any difference to me since the price difference was a few Euro, but its good to compare apple to apple
1. Since you want to visit Tsavo & Amboseli, it's best to book from MBA. It's only 4-5 hour drive from MBA.
2. When you're in MBA, try visiting a few Tour Operators. Have a look at Kuldip Tours.
3. Mara is too far out from MBA, you will need to take a domestic flight.
In short - head out to MBA & book safari when you are there thro' a local TO.