ALL trumpet students ask the question: "What should I practice?"
1. You should practice what you can NOT play. After all practice is for improvement.
2. Legato songs. Everybody can play a march style. The song style is what makes the trumpet an instrument.
3. Light, soft, smooth and connected tonguing. As close to slurring as possible. If we work on the hard stuff then the easy things take care of themselves.
4. Sightreading. Nobody likes it but you can't play without that skill.
5. Transpose for c trumpet. Play out of
the church Hymn book.
As far as method books go if you have the Arban or Williams then you are fine.
The Max Schlossberg Dailly Drills will give you a good workout as well. To go through it do 1 exercise and skip 9. Go from cover to cover. 1, 11, 21, 31, 41, ...... to the end. The next day play 2, 12, 22, 32, 42..... The book is played through 3 x times a month that way and everything is covered.