Although it is not a must, but remember an emissary's mission is usually to negotiate or to gather information. So in my opinion it is best to send an emissary to a people whom he can associate with. For example a president sends a trusted emissary to a war-torn region to discuss peace terms. Take for example sending a Muslim ambassador to Vatican? Yes, he will carry out his job, but at a limited perspective. But it is not a must.
So apart from professional experience, an ambassador will be more effective if he understands the languages spoken, the culture, etc etc.
So this is something to put into consideration unless the only objective is to rewards his friends, then you can pick anyone and randomly send