Many band programs start their beginners on cornets. When I started in beginning band, the band director told me he wanted my parents to get me a cornet. I thought I was playing a trumpet. They work the same, but they are easier to hold. I started on one, and every program I’ve taught in recommeded them for their beginners.
The main advantage of a cornet is that they are easier to hold up which helps prevent many embouchure problems from starting. Over the years, I’ve noticed that many of the students that develop embouchure problems started on trumpets. In the end, I advise that you use what your band director recommends.
I recommend the Bach CR300, the Getzen 580 Cornet,the Yamaha 2310II or the Yamaha Standard Cornet. These are all high quality beginning band cornets.