MySQL Server 5.7.33 or upgrade
Support
The 5.7 release is still maintained, and has support until October 2023. So there is nothing that makes it a bad idea to use it for Production.
However, if you are starting from scratch, using 8.0.23 (the newest release in the 8.0 chain) will get you some new features, and support until April 2026.
Security
If 8.0 was bleeding edge, a case could be made that it is likely to have more yet-to-be-discovered security vulnerabilities than 5.0, while the 5.0 release chain has had more time to find and patch them. But because 8.0 has been around for 2+ years, I think it is not likely to suffer from that problem. And other than bleeding-edge considerations, the newer version is probably more secure.
Performance
A benchmark from severalnines.com indicates that 8.0 is quite a bit faster than 5.7.

The benchmark results reveals that there has been an impressive improvement, not only on managing read workloads, but also on a high read/write workload comparing to MySQL 5.7.


Overall, MySQL 8.0 has dominated MySQL 5.7 efficiently.

General
And the MySQL marketing materials suggest that 8.0 is better in many ways.

MySQL 8.0 includes significant performance, security and developer productivity improvements

Summary
5.7.33 would be fine, but unless you have a specific reason to stick with 5.7.x, go to 8.0.