Instrument - Rent or buy it from a local music store.
DON'T BUY INSTRUMENTS FROM AMAZON, EBAY, WALMART, COSTCO, ETC - THEY ARE TERRIBLE!
Bach 7C trumpet mouthpiece - This is highly recommended! A lot of beginner trumpets come with a mouthpiece that is too small and it can make learning the trumpet more difficult as a result. All local music stores should be able to get you this mouthpiece. If not, order it online.
Music stand - to use at home for daily practice. Don't get the cheap, flimsy folding metal music stands - they are garbage. Here are a few suggestions - music stand 1, music stand 2, music stand 3. Your local music store will also have similar options.
Instrument maintenance / care kit - all local music stores should have something like this
Extra valve oil - I recommend Blue Juice or Al Cass brands.