It depends solely on the number of people you want to survey. However, you need not worry too much that the invitations will put to heavy a load on your visitors. There´s two really good control mechanisms build into the UserReport system.
1. You can adjust your invitation rate (the proportion of visitors that receives an invitation) in realtime. You can adjust the rate so anywhere between 10 to 100 % af your visitors receive the invitation. That´s a really nice feature. The feature allows you to invite all visitors if you are a small site (for instance a blog) or a very small proportion if you are a huge site.
2. The UserReport system is built to ensure that no one browser get´s more than one UserReport invitation per site per three weeks. Read more about survey quarantine rules here.
Based on this, don´t worry too much about turning up the invitation volume. You´re better off focusing on the number of interviews you need to cover your research needs. That´s the second part of the question.