Cheapest approach is likely going to be that USB-C to USB-A cable.
Or making an appointment with Apple, if they're willing to perform the transfer, and bringing it all in.
Alternatively, get a hard disk drive to use for backups your new computer, and use that (initially) to back up the old iMac.
You'll also need a USB-C to USB-A adapter for the new iMac, and a hard disk with a USB-A connector.
Using a SuperDrive is going to be a whole lot of work, and all of that work manual. DVDs are 4.7 GB or so. Tiny.
If you do choose to use SuperDrive and manually transfer the data ~4 GB at a time, you will need the Apple USB-C to USB-A adapter to provide enough power to run the SuperDrive on the new iMac.
The hard disk will allow you to get Time Machine backups of your new iMac, as well.
If you decide to get the USB-C to USB-A cable for the initial transfer, you can get a USB-C hard disk for Time Machine backups for the new iMac.
PS: The only way to indicate data is valuable is with a backup. No backups means the data is one command mistake or one hardware failure or one hardware damage away from total loss.