If you have no extra plans, then about $500, £250, or €400 should be plenty, depending on how much souvenir shopping you wish to do. That should cover your visas, the tips, the restaurant bills on the days in town and some small gift shopping. There is plenty of opportunity for buying hand crafts, beautiful stone and wood work, new or ancient African masks, etcetera. If you plan to do so, bring enough cash. Some places except visa (with commission), but not all. If you are planning on some extra days before or after the itinerary, most last minute travel arrangements have to be arranged by cash, so please take that into consideration as well.
The best place to buy souvenirs is on the Kenya side of the Namanga border between Tanzania and Kenya, when you are re-entering after climbing Kilimanjaro. The souvenirs are sold there directly by the people who make them and they come up to your car and sell them themselves. The prices are excellent (perhaps 1/2 of what you may pay elsewhere) and the people only take cash (Kenyan shillings, which you can exchange yourself as you learn the exchange rates).