Bryan,
Wrestling is not a sport I typically shoot and I did it once to catch senior night for some of the kids who also play football. I found that 1/500 was fast enough to freeze most motion but the lighting was sufficient that I went to a more comfortable 1/640 using a f2 lens.
Now that almost every camera body features auto ISO, I shoot all sports in manual mode where I select aperture and shutter speed and let the camera choose the ISO to compensate. With wrestling, you MAY be able to also manually set ISO if the lighting is even across multiple mats but that will depend upon the venue. You can limit the maximum ISO it can choose automatically to prevent it from choosing a value that creates too much noise/loss of detail. Check your setup during warmup prior to the match and decide if you need to drop to 1/500 or even slower to keep ISO in check but I would not want to go slower than 1/500 if you want to catch any relatively fast action.
Shoot in RAW, this will allow you to recover from a lot in post and it will allow you to do the most with noise reduction after the event. The only time I shoot in jpg is when I get a new camera body and forget that Canon sets the default to jpg output. The first two test images with my 1DX III were in jpg before I realized the default; it hasn't been used to create in camera jpeg files since.
My rationale for going manual is that I know I have to choose a shutter speed sufficient to freeze action and with most sports lighting I will be shooting with aperture wide open. Before auto ISO was a feature of most bodies, then shooting Av priority made sense because you had to manually select ISO and then let the camera choose as fast of a shutter speed as possible but auto ISO is going to provide better results with auto ISO available. I haven't shot a sports event using anything but full manual with auto ISO since upgrading from a 1D Mark II to a 1DX many years ago.
Wrestling is definitely a different event to shoot and I didn't realize I would be doing so until 30 minutes before it started. Not much time for research and I had never even watched wrestling prior. But here are some examples of what 1/640 will do. I would have loved to have had more time to learn proper photographer positioning because location is critical. I have that down for football, soccer, and basketball but definitely not for wrestling.
The first two were shot with a 1DX II / EF 200 f2 setup @ 1/640, the last with a 1DX / EF 135 f2 @ 1/500 and 1/640 would have been a better choice.
Rodger
And if you get floor access, remember that officials love to have photos also which is a good way to gain good diplomatic cover and have them watch out for your access. When I shot the senior wrestlers, it turned out to also be the official's last match before retirement and he really appreciated getting several photos from his final match.
I shot a HS soccer match Saturday and the head ref told the two linesmen to look sharp because they would get some good photos of themselves from the game. I didn't disappoint them and they took care of making sure I had the access I needed and also fed me during the half.
Joe Namath did Isotoner gloves commercials for years with the the tagline that they took care of the hands that took care of him. Taking care of the officials and coaches will make your event access much easier and more enjoyable for you.
Rodger
