What do you mean by "high speed"? Are you referring to capturing footage in high frames (60 frames per second or more) so as to end up with slow-motion footage? If so, you'll find that your current budget will be extremely limiting, if not impossible to find something. Newer gear or older used gear at that price point will probably be limited to 30 frames per second maximum.
If by "high speed" you're simply referring to your subjects moving (sports), then any video gear should suffice. Though I would explore camcorders if all you intend to work on is videos. If you also need gear for photos though, then for your budget, you'll most likely be looking at used DSLRs. Canon's most inexpensive R-series camera (mirrorless) is the EOS R100. There's a kit that includes the RF-S 18-45mm lens for $599.
Right now you can get the EOS M50 Mark II refurbished with the 15-45mm lens for $479 U.S. from Canon's refurbished store. It can record up to 60fps in full HD (1080p) resolution. You might want a longer lens at some point, especially for outdoor sports on a large field.
12/05/2023: New firmware updates are available.
09/26/2023: New firmware updates are available.
08/18/2023: Canon EOS R5 C training series is released.
07/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
03/30/2023: New firmware updates are available.