For formal introductions, use English unless all the people involved share another language. In casual greetings, however, try out Swahili. There are a number of beginning Swahili books, and almost any travel guide will have a list of stock phrases. Take the time to learn the correct pronunciation, and that will clearly indicate to anyone within hearing distance that you are a cut above the average foreign tourist. When you extend yourself a bit more than others do, you won't have any lack of teachers.
Most African languages are easy to learn for that reason.
What is true of Swahili is doubly true of other indigenous East African languages. No matter where you go or what you do in East Africa, you will invariably be involved in some kind of bargaining situation. Some stores have fixed prices, but cost is usually a matter to be settled between you and the seller. The fact that you are obviously a tourist will tip the scales against you, and the seller will be trying to get the best possible price, which is only to be expected. One of the valuable functions of bargaining is that it tends to level out economic disparities.