Firstly, I assume you mean 'milling bit' rather than 'drill bit'? A milling bit can cut sideways (radially), whereas a drill can only cut straight down (axially).
Step and Direction
There are two types of stepper motor drivers.
One type has two digital inputs, 'step' and 'direction'. The controller makes the motor move one step by sending a pulse (high then low) to the step input. The more often it sends pulses, the faster the motor rotates.
The other type has four digital inputs '1', '2', '3' and '4'. To make the motor rotate is slightly more complex:
The board you've chosen uses an L298 stepper motor driver IC. This is one of the 4-input types.
I assume you're using a PC running Mach3 as the controller. I believe (though I may be wrong) that Mach3 only supports the step & direction type of stepper controllers.
The other thing about the L298 is that is doesn't support microstepping. This isn't strictly necessary, but it's a great thing to have. A microstepping motor driver will actually be able to rotate the stepper motor by fractions of a step, often as small as 1/16th of a step. It does this by carefully controlling the current in the motor's windings in a sin / cosine fashion. As you can imagine, this improves the resolution of your system greatly. But it also has other benefits. It actually improves motor acceleration, and prevents strange resonance effects you can get with steppers at certain speeds.
Take a look on eBay some more. Definitely try to get a board with step & direction inputs. And if you can, get one with microstepping, even better.
Based on what can be gleaned from the website you linked you ought not to exceed the phase current specified. This is how I see but if you can find proper data sheets, they might tell a different story.
Firstly look at the torque-speed curve (linked on the page): -
If you do the math, you'd calculate that the maximum mechanical output power is about 1 watt (100 rpm and 0.1 N.m = 1.047 watts). This is about the same at 200 rpm ( 200rpm and 0.06 N.m = 1.26 watts). At 400 rpm output power is 0.837 watts hence, you can see the max output power is 1.26 watts.
With a coil current of 0.31 amps per phase and a coil resistance of 38.5 ohms (as stated), the power (heat generated not mechanical power) is 0.31^2 x 38.5 watts = 3.7 watts and this means your stepper motor can be running quite hot.
Having said that, this "apparent" inefficiency (some simplification and assumptions made here) of about 25% will not be at optimum mechanical output. At optimum power output ( I reckon about 100rpm), the power in will be about 2.1 watts assuming a peak efficiency of about 60%. This is about "normal" for steppers of this type.
So, if you are always going to be running about 100 rpm, the current into the coils will be lower than 0.31 amps BUT, the details in the link are really unclear about this so caution should be taken.
Conclusion - I don't think you can dare run the coils at more that 0.31 amps based on what the specification says. I recommend finding out more about the device. Try looking at one from a regular supplier i.e. one that has a proper pdf data sheet and deciding what information that data sheet provides that this one doesn't.
I'm not familiar with the raspberry-pi, but there's a good chance the stepper motors draw more current than the GPIO pins can supply. It's better to supply these motors with their own power supply.
Depending on what voltage your motors require, you can use AA batteries. If the motors require lots of current, you may be better of using a LiPo battery of the appropriate voltage instead.