You won't be able to use Mach3 to control the TM signal generator directly. Mach3 uses the parallel (printer port) on a standard desktop computer to control whatever device you are controlling. TM stuff uses the serial (COM port).
I just upgraded my TM1 system with the MP3000 DTHC and used my old Torchmate (Flashcut) motor controller. There was a minor mod required to the motor control box (translate some wires on the DB25 parallel connector) but it works fine.
The MP3000 is a much better box (actually combination signal generator and breakout board) and it can control in three axes (up to 6 actually) with digital torch height control. For $850 with a liscensed version of Mach3 - it's money well spent and I really like the new setup.
This setup will also require a floating torch head to take full advantage of the DTHC, but can be used with any torch head mounted on a Z axis. The MP3000 with the Mach3 is a really powerful combo. I really haven't even done much cutting with it yet, but I alreadly like the Mach3 interface much better than the standard TM stuff.
Mach3 will pretty much take over your computer and you won't be able to run it on a laptop - it HAS to be a desktop to run and be consistently stable. In fact, Mach3 install process pretty much has you strip WinXP down to nothing before install. Mach3 works at a very low level on the computer and any extraneous interrupt requests from some TSR program will cause it to glitch. So that is something to consider. But once you use it, you'll see how much better it is controlling your plaz system.