Many manufacturers nowadays sell their instruments without cases: however, you do need at least a gig bag. As is the case with most instruments nowadays, there is a large variety of cases and bags available, with or without backpack straps.
For players who do not have the strength to hold the instrument for any length, or for those who use it in marching, carrying straps are a good idea.
Stands prevent the instrument from falling off chairs or other surfaces. They keep your horn safe - and allow for complete drying.
Once you have mastered your first pieces, you'll probably be looking for equipment to vary or expand your repertoire. We suggest you get some information on the many different mouthpieces available, test out some of them and then decide on one or more.
Finally, something to put onto the bell of your instrument: mutes. They are indispensable to achieve a wide a variety of effects in your orchestra.