Thanks - no access to Windows PC so I'll miss that.
Please explain Boot into Internet recovery
Newer Macs can boot from firmware and download then install the OS even to a new, blank drive. You can read about it
here. The only issue is it install the version of the OS that came from the factory. So if your Mini shipped with Mountain Lion, then someone added Mavs later, Internet recovery will give you Mountain Lion. Given you bought this used, I highly doubt it is new enough to have come from the factory with Mavs.
Just to make sure don't get stuck without access to Mavericks, I would start the new machine and launch the App Store app and "purchase" (free) Mavericks under your AppleID. If you command-r boot off the Mini now it will allow you to reinstall Mavericks since it has a Mavericks recovery partition on the drive, but it would ask you for an AppleID to do that. Once you have made the purchase with your Apple ID, you can use that to install Mavs.
Here is what I would do.
Start the new Mini as is and purchase Mavs in the App Store.
Command-r boot the Mini to recovery then start Disk Utility and erase only Macintosh HD. Quit Disk Utility then click reinstall OS. This will ask you for your AppleID then DL and install Mavs.
Once that is done and the system reboots, create a temp dummy account for yourself and login to it. DL and install the free 30 day trial of the app Carbon Copy Cloner.
Now install the new SSDs. Put you old 256GB SSD in a USB enclosure and option key boot to it. Start Disk Utility and format the new SSDs in Mac OS Extended format. Then start Carbon Copy Cloner and clone the OS from the external 256GB to one of the new internals.
Shutdown then disconnect the external. Once the machine starts go to System Prefs and select the new SSD as the startup drive.
Now launch Migration Assistant and use that to import your data from the iMac. Give
this a read first.
If you have too much data on the iMac to migrate it all to the Mini, in Migration Assistant you can uncheck what you don't want to move (like maybe Music) then manually move it later to the second SSD.
This migration will import your existing account from the iMac. After the migration logout of the temp account and login to your existing account that came over. Poke around to make sure everything looks okay then you can delete the temp account.
