Best Connection to Migrate Files & Data from my old MacBook Pro (mid-2012) intel i5 to my new Mac Mini m4?

Are you just migrating data files or do you want to migrate user accounts, applications & other settings also?

If it's just data files then I would advocate using File Sharing to connect the two Macs via your network. Then you can use the Finder to just copy the files from the old Mac to the new Mac.

If you want to migrate user accounts, apps & settings then Migration Assistant is the way to go. The "connection" for Migration Assistant can be WiFi or direct ethernet cable between the two Macs.

DO NOT use a USB cable to connect the two Macs!

I have always done migration from a Carbon Copy Cloner backup.

For the family I have done restore with Migration Assistant from that CCC backup because I don't know all the places they might have their important files (and their Desktops and filing workflow can be very messy).

But personally I know where important files are. So I have done it by manually after a clean install by copying user data files from CCC backup's Home folder, and selected items from ~/Library (Mail, selected preference files from apps like GraphicConverter or BBEdit, 3rd party support data files from apps like WiFi Scanner or coconutBattery) and from /Users/Shared (VMware Fusion Virtual Machines, previously Photos library was also there, now on external disk). Then install important 3rd party apps. Yes, this takes about 2 hours and via Migration Assistant the end result is about the same with less fuss.

Time Machine backup should also be OK but AFAIK it is not so handy for manual copy as CCC.

I guess also via Ethernet or Target disk mode it should work. But I like to have a CCC backup of the old Mac for a few weeks (just in case) so I might erase it for other purposes after migration.

Carbon Copy Cloner macOS compatibility:

https://bombich.com/download

FWIW, when jumping from a machine running Catalina to one running Tahoe, you may want to take a fresh start approach.

Many of the apps you have on the Catalina machine are likely to be incompatible with macOS Tahoe. You will need to check which ones are and consider updates, alternatives, or just forget the apps if you haven't used them in a long while. After that, download the apps and do a fresh install of the apps on the new machine.

Next, which ever method is most convenient, manually move data that you actually need to the new machine. You may find that you have a lot of stuff that simply has no purpose anymore and is just taking up disk space. Also note, most all iCloud items will be automatically transferred when you sign into your AppleID or are available for download.

Given the age of the old Mac, you have probably collected a lot of cruff and this is an opportunity to do a major house cleaning and give yourself a fresh new start.