There is no other specific preparation you need to do to upgrade to Insight 8.7. However, if you are upgrading from any version below Insight 8.4 it's very important that you follow the 8.4 preparation guide.
Specific to the 8.7 version
If using MySQL, make sure to upgrade your database driver to a 8.x version. You can find them here: https://dev.mysql.com/downloads/connector/j/