Powering a fan with an AC adapter
You should always use a supply rated higher than your target load unless you really know what you are doing, so for your project, I recommend using the supply rated for 1.2A. Also, if you can look into what motor the fan uses, it may be possible to operate it at other nearby voltages safely.
There is no single standard to which conductor on the barrel connector corresponds to VDC or ground. However, generally the device is indicated to be Center Positive or Center Negative via a symbol embossed by the connector something like:  
If your device lacks an indicator, you must take it apart and inspect the board/wiring to see which end is hooked up to ground to avoid damaging the device and power supply.