For your free trial lesson, there's no need to go out and by a webcam if you don't have one. Your teacher of course has a high definition camera, so you'll be able to see him or her clearly.
If you enjoy your trial lesson and end up continuing lessons, we do then recommend purchasing a webcam. Ones that work well can be had for about $30, and they do help student-teacher interaction. We've found that Logitech brand has generally been a good option.