Which OSX is the best for a Late 2013 iMac

In theory, a Late 2013 iMac could run the currently latest version of macOS Catalina. However, a few things may make it not a great choice, and those are:

1. Are you dependent on any 32-bit critical apps? If so, and there are no 64-bit updates for them, you will not be able to run them under Catalina.
2. How my system RAM does your iMac have? To run any version of macOS, not just Catalina, you will want at least 16 GBs.
3. Does your iMac have an SSD or HDD system drive? You would want an SSD for Catalina for the best overall performance.
4. Related to the 3rd point, how much free space does this drive have?
5. Do you use any third-party peripherals with your Mac? If so, check with their suppliers to verify that they can be supported under Catalina.

Not trying to "turn you off" to Catalina, just wanted to make sure you are aware of these things. Actually, they would be true regardless of which version of macOS you decide to upgrade to.

Ref: Upgrade to macOS Catalina - Apple Support

I think High Sierra/10.13.6 is the best & least buggy.

I continue to run Mojave 10.14.6 (18G6032) on my Late 2013 iMac. Even though it has an internal SSD, and plenty of RAM, I prefer Mojave over Catalina, as I need to test certain features and applications in both Mojave and Catalina (which resides on another Mac).

I have a late 2013 27" iMac that runs Catalina just fine with no issues at all.

I do however, have 32GB RAM and an SSD.