I'm actually running a 120A, 130kV, 6.5kW rated (yeah right) motor from a 100A ESC, currently on my micro lathe but I have used it on the router - somewhere in this thread. This motor is good up to 50V, so I should use a HV ESC to get the full speed but I've not got round to buying one. The rigidity of the micro CNC lathe limits the power draw somewhat as it's not rigid enough, so it will only draw a few hundred watts. If I use the motor at a low speed with a big drill it could be more. I leave the PSU at about 24.5V, but it's really not critical so long as it's not above 4.2 volts per cell (i.e. 6*4.2=25.2V). It's nice to have the lab PSU, but it's not worth buying one just to power a spindle. Down to about 23V would be fine as far as the battery's concerned.

The listing for the ESC states 22.2V - this is because they expect people to use Lipo batteries, which are nominally 3.7 volts per cell so a 6 cell battery is 22.2V. However when fully charged the same battery will be 4.2*6=25.2V, so the ESC will withstand 4.2V. Since it's a cheap one it would be prudent to run a little below that.

I read somewhere that hardwoods take about 7W/cc/min to cut, so 108*7=756W. That makes 18cc/min about 18*7=126W. Bear in mind since this is motor output power we need to include the efficiency of the motor.

The motor I linked to was based on 12000rpm, but with a 6mm cutter you could be using almost twice that? I've cut some hardwood, not sure what it was, with a 6mm single flute carbide cutter at 6m/min and 6mm depth of cut and 20000rpm. However if you're machine can only manage 2.5m/min then a lower spindle speed is fine, but perhaps aim for 18000rpm? Although having said that the motor is most efficient when at maximum speed.

Anyway, if it's 126W and even if we double it to make sure, at 250W then you've got plenty of options for the PSU. At that power the battery is hardly necessary, but it would make a very robust system if you did have one. I'd mount the battery and ESC on the Z-axis as close as you can to the motor to keep all the wires short, then have long wires from the PSU to the motor. This will make the ESC run more efficiently, i.e. cooler and in extreme cases can make the difference between it surviving and not.