I always recommend that, if possible, a beginner starts on high quality instrument, especially the high end Yamaha and Bach trumpets. Better quality instruments make it easier for students to achieve success, especially with making a good, characteristic trumpet sound. While it is a bit more expensive, there are good used trumpets for around $1000, and I'm always happy to help look for good options. A word of caution- always check with a knowledgeable professional before springing for a deal on eBay!
If buying a used trumpet is not an option, there are many reputable music stores that rent out instruments to beginners. I prefer the Getzen student line. Here are some links to area music stores:
The focus on beginner lessons should be on creating a strong fundamental base, made up of a good characteristic sound and an understanding of breathing, articulation, and posture. While the process may seem slow at first, this sets up the potential for exponential growth and more rewarding experiences in the not-so-distant future.
Why start beginner lessons?
While music teachers are more than capable of teaching your student how to play the trumpet, they have dozens of students to teach at the same time. And not all music teachers are experts at every isntrument. With private lessons, your child gets the one-on-one attention to propel him or her forward, having formed great practice habits and proper technique from the beginning of his or her adventure in band.