Well, I’d like to see you personally get it done in 3 months with starting with 0 ROS or robotics knowledge 
If you’re going to ever do distance sensors, you have 3 options:
- The best: laser range finder
- Close second: 3d cameras (kinect, intel euclid, intel realsense)
- Last resort: proximity
Given your price range, I’d try and go for #2 if it fits the budget, and don’t bother with #3 other than for proof of concept/want people to feel the pain while learning. Actually a combination of them all would be a good way to demonstrate that your algorithms are theoretically bounded by the quality of your sensor data =)
Pito, design the course and what you want to show first. The robot you need will be decided by that. If you are unsure of what the course needs in it/how to go about that, lets take this offline/another thread. I’ve built many a robots and i think I can help you here with coming to a close on what you need to show the students.