We've figured out how to operate both the solenoid and vacuum pump brushless motor from different pins on the same Arduino shield! The motor can simply turned on or off by supplying 5V from a MOSFET on the Arduino shield.
As for the pressure sensor, we've connected the positive lead to Analog pin 0 and ground to ground. We're using a code which either opens or closes a solenoid depending on whether this voltage on pin A0 is greater or less than 5 volts. When running the system at atmospheric pressure, the solenoid began sputtering wildly. We're not sure what the voltage scale on the pressure sensor is, so we don't know whether we should expect the solenoid to be open or closed at this pressure. We're considering using the serial monitor in Arduino to see what voltage is being supplied from the pressure sensor to the pin at this pressure.