If you are responsible for stocking a school or a similar business that requires the purchase of a large number of headphones, then there are several criteria that you will want to look out for.
First, you will want to decide what type of headphones you are looking for.
Earbuds are extremely common for personal usage, but aren't quite as popular for shared usage. They probably aren't a viable option if you plan on using the headphones in a classroom setting, since they aren't very sanitary.
On-ear headphones are somewhat of a hybrid between earbuds and traditional headphones since they incorporate separate speakers with separate cords for each ear, like earbuds, yet are connected via a bridge that rests atop the head like traditional headphones. These are extremely common for classroom usage since they are generally a bit cheaper than traditional headphones. However, they also tend to be quite fragile and susceptible to damage.
Traditional headphones are probably what comes to mind when you imagine headphones: two large speakers with padding connected via a bridge that rests atop the head. They can come in wired or wireless varieties, which each have their own advantages and disadvantages. In general, traditional headphones are very sturdy and have high audio quality, yet are more expensive and cumbersome than other options.
Wired vs Wireless
Wired headphones don't suffer from spotty connection issues that you can sometimes get with wireless devices, especially if they are of lower quality. They also tend to be cheaper for the same durability and quality of sound. Finally, they don't require batteries or recharging.
On the other hand, wireless headphones avoid the irritation of cord entangling, which makes organization a much easier prospect. On top of that, the rise in popularity of wireless technology means that the price for wireless headphones is rapidly falling. You can easily find a quality pair of wireless headphones with the same level of quality as a wired pair for only a slightly lower price.
Finally, you will probably want to look for a company that will offer a bulk discount. Many headphone retailers sell in bulk to businesses and schools, so they might offer a cheap classroom headphones discount if you buy a large quantity. As an added bonus, some of these companies probably also sell other goods and services that your business might be interested in, such as microphones, keyboards, mice, and webcams.