Why are certain aneuploidies more common?
I thought it was just that the other aneuploidies were fatal. They occur as often but miscarry earlier in the term therefore you don't see them. So basically there are only three that are viable 21,18 and the sex chromosome with a number of combinations: XO, XXY, XYY and XXX.

More information here:
http://www.nature.com/scitable/topicpage/chromosomal-abnormalities-aneuploidies-290

With regard to the frequency for each chromosome:

For males (i.e., sperm; source):


  The mean disomy frequency is 0.15% for each of the autosomes and 0.26%
  for the sex chromosomes. Most chromosomes analyzed have an equal
  distribution of disomy with the exception of chromosomes 14, 21, 22
  and the sex chromosomes, which display significantly higher disomy
  frequencies.


Size of the chromosome is frequently reported as a factor in the frequency.

For females (i.e., eggs; source):


  The data is obviously harder to attain. One study from IVF treatments
  show differences in the frequency of different chromosomes at
  different stages in meiosis.