SSRS upgrade to 2014

This question is off-topic in my opinion and would be better fitted on dba.stackoverflow.com than here, nonetheless, if you have SSRS and SQL Server Instance on separate servers, then there should be no difference which one is upgraded first.

When it comes to database, I would recommend clean install and restore from backup instead of in-place upgrades which can cause some issues.

I personally have not worked enough with SSRS to know its quirks and can not speak to the validity of in-place upgrade vs migration. I would recommend researching this further to prevent critical failures.

Before any upgrade, make sure you have solid back out plan incase something goes wrong. Are you going to have 1 weekend to do it or entire month? If you can not meet deadlines, how is business going to access data and reports? If everything fails and you can not bring new instances online how are you going to restore to the pre-upgrade state? Are you going to test this on non-production environment first? This is not the extensive list of questions by any stretch but should give you a general idea of what you should be asking and how you will respond to it.