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The choice will depend a lot on the application. In what environment will the robot work? What is the power and space availability? What will be the working distance of the camera?

For example for a slow-moving robot I used two webcams with rolling shutter and without synchronization, it worked quite well for the required precision.

A few things to consider:

• If your robot won't work in sunlight, a RGB-D camera (Kinect-like) is the best. It's very precise and gives you the distance in mm for each pixel. It also fits in your budget.
• For distances over 2-3m, forget the stereo cameras, you'll have to use Lidars.
• Professional systems (global shutter cameras with trigger) won't fit in your budget. A single camera like that costs at least 5-600€ with lens (2MPixels). They also need a performant embedded computer to transfer the data and get the disparity map in real time.