You really couldn't ask for a better mode of transport for Tanzanian roadscapes other than bus travel. It's usually coach buses which travel between cities; these buses are simple in offerings but they get the job done. Luggage allowances are quite standard, and bigger bags get stored in the compartment below. Make sure to hold on to smaller bags and valuables, and keep an eye on your things throughout the journey. On board, it may get a bit loud at times as drivers love to turn on music, so just make sure to bring earplugs if you know it'll bother you, especially so if you're going overnight.
Flights are the norm for travel in Africa - it allows for easy access between rough terrains. A journey with hundreds of kilometres in between can be shortened to mere minutes of flight. Keep in mind that short flights are very much not sustainable and produce a giant carbon footprint. The departure schedule is quite flexible. On board, cabins are quite simple. There are usually no bathrooms on planes since it's such a small cabin. Make sure to bring a sweater or layers with you as it can get chilly on the airplane.