Generally, we recommend PS Eye over depth sensors (Kinect and others) because of greater capture area and increased frame rate.
With greater number of cameras you create more points of view, thus preventing tracking errors caused by occlusions. That's why it is better to track more complex motions with more cameras.
3 color cameras is a minimum for the tracking to work at all, but may produce many errors, depending on captured motions. For capturing dances, I recommend at least 5-6 PS Eyes or dual Kinects.
Your laptop looks good for recording with a single first-generation Kinect. You can't use second generation Kinect (which is slightly more accurate), because it requires USB 3.0.
For 3-4 PS Eyes, CPU and memory look OK. 2x USB 2.0 ports look as a possible problem. First, you need USB hubs to even connect more than 2 cameras. Second, both ports may be internally linked to a single USB controller, with second controller used for built-in devices like webcam, network, card reader etc. In this case, you can connect more than 2 cameras, but only with a lower frame rate (30-40 fps). If you have a regular HDD in the laptop, not SSD, then there may also be a problem with disk writing speed during recording.
If you have 1-2 other laptops, you can use the
distributed recording feature to record with more cameras.
GPU usage during recording is fairly low, so integrated GPUs are usually sufficient. However, for the tracking process in Mocap Studio, the GPU performance is essential. HD 7950 seems adequate, if it performs as well as when plugged in a regular desktop.