What is the right course of action here?

You answered correctly. At this intersection, there is a stop sign and a traffic sign indicating the priority road. You must stop completely at the stop line to check for cross traffic. After stopping, you have to yield to vehicles on the priority road, which in this case is the blue car from your right. Once the blue car has passed and it is safe, you may proceed. The red car is not on the priority road and must yield to you, so you do not need to let the red car go first. Remember: always stop at a stop sign, and yield to all vehicles on the priority road.