Linux CNC, what controller / breakout board is most flexible?

Depend on the budget, otherwise, there are plenty of possibilities, so here are a few:
Mesa 7i95 for step/dir type of stepper and servo with encoder feedback
or
Mesa 7i76E for step/dir with no encoder feedback, it can be added later
or
Mesa 7i97 for analog +-10V control of velocity mode servo drives, usually for retrofits
Add a Mesa 7i73 for the panel as it has matrix keyboard, LCD, analog, MPG, digital in and out, etc, all through a single network cable.
Or go for
Mesa 7i92M
Mesa 7i76 for step/dir
or
Mesa 7i77 for analog servo
-
Additional IO >>> Mesa 7i84
Even more IO or stepgens or PWM or encoders >>> Mesa 7i74 and whatever Smart serial card you might need, up to 8 can be added to 7i74 plus another one to one of the above, so 9 in total.

There might still be a way to use the motors and encoders, there should be a converter for Fanuc encoders, but i have no idea how or where.
If the drives are OK, check if they have encoder outputs, those are usually standard incremental A/B/Z.
Tuning the analog servos is not a big deal as some tend to make it, with some good drives it is easy, simetimes it takes a while to find the right PID values.
Google for "servo tutnig detailed howto" the first result should be a link to this forum with very detailed info on wiring and testing analog servo drives.

The commutation encoding only needs to go to the drives. You can largely ignore it if you are keeping the original drives, if there is a way to control the drives.

Alternatively, you can convert the 4-pin commutation signals to various other forms of commutation signal in HAL with the "bldc" HAL module.
See the "f" and "F" modes. linuxcnc.org/docs/stable/html/man/man9/bldc.9.html

Or, for some Fanuc encoders there is a special Mesa function:
linuxcnc.org/docs/stable/html/man/man9/h...html#Fanuc%20encoder.
(But I think that is for later motors than you seem to have)

But, as I said, if you can control the drives you can ignore the commutation.