Agree with justashooter above.
Get the Sabrent USB3 enclosure.
You can also find it here:
SABRENT 2.5 Inch SATA to USB 3.0 Tool Free External Hard Drive Enclosure [Optimized for SSD, Support UASP SATA III] Black (EC-UASP)
tinyurl.com
Did you install any of the internal drives yourself?
Then, you know how to remove them.
If you DIDN'T install them, it's easy to remove them.
You'll need a Phillips #00 driver and a TORX T-6 drive to "take the bosses" off the side of the drive after you take it out. Go to ifixit.com to see the replacement guide.
Then, when you have your new MB, put the drives into the enclosure, connect it to the USBc port, and see what happens next.
TIP for moving files from an old account to a new one:
1. Connect drive and let icon appear on the desktop
2. Click ONE TIME on the icon to select it and bring up "get info" (command-i)
3. At the bottom of get info click the lock icon and enter your NEW password (that you're using on the new MB)
4. Put a checkmark into "ignore ownership on this volume" (sharing & permissions)
5. Close get info.
Now you can copy stuff from the external drive, and whatever you copy will "come under the ownership" of your NEW account. This avoids "permissions problems".