According to the last bullet on https://confluence.atlassian.com/jirasoftware/jira-software-7-3-x-upgrade-notes-861251109.html, upgrading from JIRA pre-7.0 to JIRA 7.0 first is recommended, before going to JIRA 7.3.
However, in our case, we are thinking of getting new server hardware with a different OS, so this would actually be a migration of our JIRA instance to a new server. We can do the XML export, backup of attachments and indexes, and then copy the stuff over to the new box. In this scenario, do we still need to start with a 7.0 instance, or can we start with 7.3?
EDIT: We are on JIRA 6.4.12, with Agile 6.7.12, and ScriptRunner 4.1.3.4. We have a few other small add-ons, but not business-critical like ScriptRunner for us. We do not have ServiceDesk.