I have Zoom H3N recorder and Lenovo Thinkpad X1 20HR002FMX -laptop. I think about linking the recorder to laptop to pick up voice from one end of the table and at some point have some kind of wireless collar microphone that takes audio from a teacher.
Which cables and audio equipment I should get? The budget could be at max 500 or 700 USD.
Read the directions for the recorder.
Do you mean a Zoom H3-VR? There's no such thing as a Zoom H3N. The zoom recorders are "stand alone" and do not need to be connected to a laptop in order to record. Record your audio with the Zoom and then download the audio file to the computer for editing.
You can connect an external mic/wireless mic to most Zoom recorders with the proper adapter cable.
If all you are doing is recording a class don't bother with a wireless mic etc. Just place the recorder up in front of the room near the teacher. Keep it simple.