The price of a safari is mostly dependent on accommodations. A camping safari will be cheapest, whether with a group of strangers or just your family with a driver guide; next would be cheap hotels, such as the Sopa and Serena Lodge chains. (Those tents you see pictured with the queen-sized beds inside ... those are considered luxury and are top dollar.) You can find deals and discounts during the low and shoulder seasons; however, some lodges and camps may close in the rainy season and roads can wash out. You'll pay more to book a safari in advance; though you can find deals by flying to Arusha and waiting to book your tour there, it's a riskier proposition and people have been scammed. When booking a tour online, be sure to ask if you'll need to pay additional fees once in Tanzania.
If you're planning a safari, you need to factor in weather, wildlife and crowds. The long rains take place from late March to late May and the short rains are from late October to mid-December. These are typically not popular tourist seasons. The dry season is July through October; with little vegetation to obscure your view of animals, this is high season for safaris. However, expect dust and cool temperatures at high altitudes (such as Ngorongoro Crater). The summer months of December through February are also dry and great for game viewing, but be prepared for heat. May, June and November are shoulder-season months when crowds are minimal, but spring wildflowers, though pretty, may make spotting that leopard in the grass a bit more difficult. The climbing seasons for Kilimanjaro are January to March and June to October; the best months are January, February and September.