I am looking for guidance and insights from someone with experience in making and executing a strategy for standardising hardware procurement across the enterprise. Could you share the insights gained from this process, including what aspects were successful and which ones were not?

Sure, I did back to basics. Starting with an asset management, dividing by towers from Servers (application hosting), Storage, SAP, NON-SAP, Network, PC, VIP, Cloud. Then I place an obsolescence standard with traceability naming like MXCNSP2014WIN01 (naming with all features). Then I managed maintenance contracts with vendors in order to give support for all my assets and last mile globally. That strategy give us 20 million of savings in a Mexico Corporation.

I think this is a good idea because you aren't dealing with so many different configurations/systems.  A couple things to determine is how large are you and what vendor are you focusing on.  I would have a candid conversation with the vendor about product lines and life times for those, or you're going to end up with a mish mosh of products anyway.  They other consideration is budget.  Are you swapping everything at once or over time.  We are a smaller organization with tight budgets, so it took us about 3 years to have everyone standardized.