Check if your HW is certified for 6.7 as well as all your 3rd. party stuff like Backup and monitoring. Update the later ones first and than perform the vSphere upgrade/new install as long as your HW is 6.7 ready.
First of all verify VMware ESXi 6.7 compatibility with your server platform ( Check it exactly and also generation of your Server). If nothing has been shown about it, i suggest to don't try to customize and upgrade it to version 6.7 (Try older versions like 6.0 6.5, they are still supported).
And about your vCenter (If you have in your environment) first upgrade to version 6.0 and then upgrade it to 6.7Please mark my comment as the Correct Answer if this solution resolved your problem