While I've technically been to Tanzania it was only a brief boarder crossing at the Masai Mara and a brief stop at their airport. That said I think my experiences in Kenya and Ethiopia would likely translate well.
The people are generally very friendly. We also experienced a lot of curiosity about where we were from and what life there was like.
Be prepared for disorderly lines and jostling to get to whatever is at the front of the line. This isn't necessarily rude or aggressive so much as just how they do things.
Permethrin treated clothes are a great way to repel insects. You can buy treatments and do it yourself in a well ventilated environment, send them off to be treated, or buy clothes that have already been treated.
Recommendations for safari clothes seem to be really overblown although they still seem like a good idea. When we were on safari in Kenya we saw a lot of people in regular shorts, sandles, and t-shirts.
Hotel quality varies wildly and may not include things you are used to being standard - like warm water or electricity 24/7. If this trip doesn't take care of hotels for you I would spend more time than usual looking at hotel reviews.
If you want to know about safari camera equipment a 100-400mm lens will likely be your workhorse. We had a 98-280 (70-200mm + 1.4 extender) and that worked well for the majority of our shots but we would have liked a bit more range in some situations and occasionally 98mm was too much zoom. Don't expect to change lenses though as it can be incredibly dusty. My impression of an ideal setup would be a ~25-105mm lens on one camera body and a 100-400 on a second and grab whichever configuration is appropriate for the distance. Some people recommend a beanbag for stabilization but we did not find we needed one.
Cell service was extremely reliable in Kenya and Ethiopia but for some reason neither of our phones would switch signals automatically all the time so we had to manually switch from time to time.
A common trend, partially evident above, is a lack of consistency in process. Whether this is place settings at tables (Why do I have 4 forks but my wife only has 1?) to how people are handled in official capacities (some passports were scrutinized while they barely glanced at ours) just be prepared to go with the flow
Heh.