If you follow my instructions, I guarantee a 98% success rate or better.
1. You need an external drive, USB3, USB2, thunderbolt, anything.
2. You need CarbonCopyCloner or SuperDuper (both are FREE to download and use for 30 days) -- doing it this way will "cost you nothing".
3. When the new iMac comes, take it out of the box and set it up, but DON'T press the power on button yet.
4. On the OLD Mini, connect the external drive, erase it to HFS+, and then do a CCC (or SD) "full clone" of the internal drive. This will be a record of the Mini's drive "exactly as it was" at the moment you "moved up" to the new iMac.
5. When done, power down the Mini, disconnect the drive and connect it to the NEW iMac.
6. Press the power-on button. Begin setup.
7. When setup assistant asks if you wish to migrate from another Mac or drive, YES, you want to do this, so....
8. "Aim" setup assistant at the external cloned backup and give it a few moments to "digest everything".
9. Setup assistant will present you with a list of stuff to migrate (apps, accounts, settings, data).
10. Select those items you wish to bring over and "let 'er go". It will take a few minutes.
11. When done, you should be presented with a login screen (and a desktop) that looks just like it did on the old Mini.
12. Done.