Where do we all start - that is a good question.
I have no idea about the kit you already have - this is for you to look at and decide - BUT
Mach 3 operates from a PC (which I assume you have). I do not know if you are trying to put this together on the cheap, or have a reasonable budget to play with (things being as they are).
The original idea for Mach was to output all the signals via the 25 pin LPT printer port.If your PC has one of these, then you can use it. You do not need a breakout board, but it is easier with one - just for the reason that someone else has done the hard work, and you have only to be able to fasten wires to it. I recommend a NON powered board. Mine was from Routout (which may be only available in UK, I don't know. Others may recommend any number of the various breakout boards that are available, particularly in the States. I don't particularly like them, because many have all manner of electronics added to them, and you need a manual just to understand the breakout board. These on board electronics has caused some problems, particulary missing steps. I prefer a "clean" board to which I can add what I want.
If you do not have a LPT1 port, then you can use the new Smooth Stepper as an output, and, indeed many would recommend it anyway. This fastens to your USB output from the computer (Plug and Play the in thing these days). This also has several advantages since it has all the outputs for the 6 axis, but has extra outputs for inputs and outputs to limit switches, alarms, push buttons etc (there are only 4 outputs and 5 inputs on a breakout board). It also generates on board, all the pulses for the motor axis (which are said to be cleaner and faster than the computer output) , which takes the pressure off your computer and allows it to concentrate on running your code.
Whichever route you choose, you will need drives to power your axis motors. I would recommend Gecko (only as a satisfied customer) and the range of drives is shown on their website (including ones to drive servo motors). They would appear to have the voltage and current capacity you require. I understand you can also get good advice from Gecko about what you will need to compliment their kit.
Gecko drives can be driven directly from the non-powered breakoutboard, or the smooth stepper. They have opto isolation on the inputs, therefore negating the need for such things on your breakout board.
That is enough to get you started. A breakout board, or smooth stepper, three Gecko drives. You will need some feedback arangements from your servos. I am not familiar with them so cannot comment.
This will get you going and everything else can follow in good time.