Retrofitting a CNC to MACH3 control has been done many times.
To better assess your path forward, you need to inventory your current system. Get and record the various info.
Axis motor info
stepper or servo
rated voltage amps
torque (holding, peak, continuos)
frame/mount size (if replacing)
shaft size & lenght, dual for encoder, dimensions of encoder shaft (if replacing)
+ 10 Vdc
dir +10 Vdc
dir & step
Rated voltage and amps
Armed with this information you can start searching and reading threads and start choosing a path.
If considering MACH3 also consider EMC2.
If you are looking for more turnkey or packaged kits, maybe look at Centroid, Ajax, or Camsoft.
Your journey begins.