The BMP085 and BMP180 are very accurate baromic sensors. They cost 3 or 4 dollars (inclusive shipping).
Your pressure sensor is can be a relative pressure sensor or a baromic (also called absolute) pressure sensor, but I think it is not ment to measure the baromic value. It can measure vaccuum and pressure up to 700kPa. It has 60mV output with that 700kPa.
It contains a piezo bridge inside, so the OUTPUT+ and OUTPUT- are outputs of the brigde.
You need a OpAmp to amplify the signal.
Converting it to baromic pressure is useless, since it is not temperature compensated.
If you want to, you might use the analogReference(INTERNAL) and connect both OUTPUT+ and OUTPUT- to analog inputs, and calculate the difference. The baromic value might be 300% inaccurate (just a wild guess).
As always, it's easier to buy Arduino compatiple parts, but it's also interesting to hack these parts
I'll follow your advices and study some more. Maybe if I compare the values from this sensor to a real analog
barometric meter, I understand how it compares...