Hi,
Looks like a 22 pin connector. Digikey, or Mouser may have it.
22 - 6 rows should be no more than 16 columns. You can, and will eventually probably) need to trace the circuits to get it the exact arrangement, and trace the rows/columns back to the connector.
So you need a controller with at most 22 I/O pins free, + a USB port. These are easy to come buy. "Pro Micro" is one popular one.
From there pick any decent software:
TMK
https://github.com/tmk/tmk_keyboard QMK
https://github.com/qmk/qmk_firmware a superset based upon TMK
Easy AVR
https://github.com/dhowland/EasyAVR)
I don't know if any of the software is better at "ghost key" elimination than the others.
You'll need to tell the software which pins you're using for each row and column. D0,...
Then you need to tell the software which key is at each row/column intersection.
There are many samples of this and it's all well documented.
I guess other options for cases include custom (laser) cut acrylic, usually 4-6 (as I recall) layers, or wood works too.
Good luck! I'm sure you'll find us a group that's generous with our experience.