You have to remember that linear voltage regulators such as those are not very efficient as they use a pass transistor to regulate thevoltage and excess power is disipated as heat in the transistor.battery supplies and designs for low power are better done with switching regulators,boost or buck,which are more efficient but have the drawback of using more components and usually needing inductors.
The capacitors in the linear supply do two things,they act as resevoirs to reduce the effects of short term transients in demand,they also act to stabalise the regulators which can sometimes be marginaly stable.So you usually find large resevoir capacitors ,a few hundred mikes,on input and output,and smaller capacitors of a few mikes or less in parellel with them.
the VA rating used is just a scalar value,it does not take phase into account,its just a rating which says the transformer can supply 12v at 250 ma