Tanzania is generally rather safe.

Some basic advice :

Don't drink the tap water - but you can eat nearly all the food.

Do care about mosquitos - as well as your anti-malarial treatment, the best remedy is being bitten as little as possible - this means nets, spray, long sleeved clothing in the evening and so on.

Don't be paranoid about crime. But do be careful around bus and train stations, ports and in Dar. It is safe to walk around at night in Zanzibar, but probably best to keep this to a minimum, as in any other large town or city.

Don't put on barbecue sauce deodorant before sleeping next to an elderly lion. In fact, barring an act of stupidity, you will almost certainly not be eaten on your trip, but bear in mind that elephants move very quickly and it is always a good idea to avoid crocodiles.