How do I transfer data from iMac to Mac mini M4 using migration assistant?

Contacts, Safari bookmarks, Notes, Keychain Passwords and other data you have saved to iCloud should automatically copy to the new Mac when you enable iCloud. But occasionally I have had to turn some item like Safari bookmarks OFF/ON to kick it in action and to update on some other Mac. It is possible to export many of those as off-line data files (just in case) but I have not done that. Passwords is an exception because I use also KeePassXC local file to store most important passwords (just in case).

You can copy local Mail by copying (or zipping) ~/Library/Mail folder. Then in the new Mac (YMMV so adjust if necessary):

System Settings > iCloud > iCloud Mail: ON.

System Settings > Internet Accounts > Add Account... > Google [log in]: Mail only.

Applications > Mail.app [wait for Mail to download online Mail and gmail]

Mail > File > Import Mailboxes... > Apple Mail > choose the old ~/Library/Mail folder > choose all Items.

On the left-hand-side under "On My Mac" > Import, ..., look for and move "Local" and all mailboxes inside it up under "On My Mac", move also "epshp" up under "On My Mac". Right-click and delete "Import" Mailbox (it has gmail mailboxes that are online).

I usually download and re-install fresh versions of 3rd party apps (a good time for spring cleaning). Many tiny apps are self-contained in /Applications but some with installers might copy their support files who knows where so IMO it is best not to just copy such apps to /Applications from the old Mac.

You cannot use Migration Assistant unless what yo have stored on the old Mac is well under 512 GB. I would strongly recommend returning the MM and getting one with 1TB SSD. Then follow the steps in Setup Assistant and Migration Assistant - Apple Community

You can manually copy the files. A tidy filing system helps with that so you know where your important files are. Preserve the old setup a few weeks until you are sure you do not miss anything from it. You might use Carbon Copy Cloner (or Super Duper) to clone it to an external disk so you can just mount it to the new Mac and copy the files.

Remember that some files are in the invisible ~/Library folder, most importantly local Mail (if you use local mail instead cloud). You might also have to re-install and configure some apps (I have archived some 3rd party app preference files and their support files from the ~/Library so I do not have to re-configure them).