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IBM zSeries mainframes are an interesting beast to work with. Unfortunately for the homelab, your options are very limited to work with, and can be questionably legal at times.
For physical hardware, it's out there - your *best* way to obtain zSeries hardware is most likely government surplus auctions. See I Just Bought an IBM z890 - Now What? for an example.
For software, you can emulate parts of most zSeries kit with the Hercules emulator, however, IBM will not license software such as z/OS or z/VM on Hercules. There are ways to run z/OS on Hercules, but is left to the reader to research.
A more expensive option that is IBM blessed is the IBM zPDT (Personal Development Toolkit), which runs around $4-5000 a year and includes software licensing.
IBM Redbooks are a great resource. Suggested reading includes: