You really only need some type of machine to run a gateway (if you need it). Basically, any machine that will run one of the following OS's will run the gateway:
Windows 7, Windows 8, Windows 8.1, Windows Server 2008 R2, Windows Server 2012, Windows Server 2012 R2
If you only use the Service and do not require a gateway, there is no server/computer involved, it is all cloud-based.
Proud to be a Datanaut!
The Power Bi Pro service is only offered through Microsoft. There is no support for a "DIY" Power BI server. Go to the ideas page and vote for that feature, the Power BI team has been amazing at answering feature requests and getting them across the finish line.
On-prem Power BI hosting is on the roadmap currently. Based on what I've heard in webinars from Microsoft, it will likely be a part of SSRS 2016, but not in the initial release of SQL 2016. The new direction from Microsoft is that CUs will be recommended updates moving forward, and often there is new functionality in these (e.g. the CU that allows live browsing of Multidimensional models from PBI).
It sounds as if there will be new functionality in SPs and CUs for SQL 2016. I would not be surprised to see on-prem PBI hosting as an update.
Additionally, on-prem Azure is in the pipeline as well. Microsoft will license the entirety of its Azure infrastructure to be hosted on-prem. This will likely include Power BI Service.