Once you have successfully upgraded your vCenter server to version 6.7, you can start with the ESXi servers.
It is crucial to check that your hardware is supported in the targeted version of VMware vSphere by using the Hardware Compatibility List (HCL). Over time, some older hardware platforms will no longer be supported in the new vSphere releases.
The ESXi Compatibility Checker Python tool can be used to verify such compliance for you in an automated way.