I'm currently advising a client right on exactly that kind of customer service integration.
Look into Live Ninja (https://liveninja.com/). It brings together the best of both worlds from web and a call center. Voice + Video + Instant connect without any special software, or a phone. You can have either one way, or two way video, and text chat too.
Obviously, get nice uniforms for your call center guys if you haven't already.
Simple, first understand the user need and their day to day activity/task and mental model. This will guarantee you best ROI.
Check following links theses will help you to understand best UX practices: