Migration does not erase the data on the source computer. The new computer will only have the old computer's Home folder, although it can transfer third-party applications and support files.
The new computer will be running Catalina. Mirroring the two may not work if the old computer is incompatible with Catalina. In fact, Catalina cannot run any 32-bit software, so before you start migrating, it would be a good idea to upgrade any 32-bit software to their 64-bit versions, if they are available. Also, there may be a future issue with Legacy Extensions which will not be supported after Catalina.
If you have not yet unboxed your new iMac, I suggest you migrate using the Setup Assistant that will run when you first turn on the new iMac. It tends to be more reliable than Migration Assistant.
How to Use Migration Assistant with macOS Catalina
Setting up a new (or repurposed) Mac- 2 Migration Assistant
Setting up a new (or repurposed) Mac- 3 Manual migration