Hy Andrew,
The specification sheet for the LM78xx and LM79xx says the minimum load current is 10mA. So provided your load is 10mA, or more, the output voltage will be correct. But if you test the power supply by itself, say for development and fault finding, there is a chance that the output voltage will be incorrect so it is a wise precaution to fit the current drain resistors.
There is also a minor advantage in having a current load physically close to the regulators.
A 1000uF reservoir capacitor will be adequate for the -9V supply but we do not know what the current drain on the positive reservour capacitor will be because I don't think you have defined what the amplifier is that runs off the 12V supply. The value of the reservoir capacitor will also depend on the characteristics of the transformer. If you post this information I will be able to give a definitive answer.
If the amplifier running of the 12V supply is an audio power amplifier I would suggest that a reservoir capacitor of 4,700uF (4m7mF) would be a good choice for the positive output from the bridge rectifier. In case you are concerned that there will be some kind of problem due to an unbalance, with the two different values of reservoir capacitors, don't be; there will be no problem.
spec