Neil deGrasse Tyson makes some interesting points in relation to this: (1) The five most common elements in the solar system are hydrogen, helium, oxygen, carbon, and nitrogen. (2) Of all the elements, the one that makes the most compounds is carbon -- there are more compounds containing carbon than all other compounds of all of the other elements combined. (3) Life on Earth is made mostly of H, O, C, N, plus some trace elements, and is based on C. ("Organic chemistry" means the chemistry of carbon compounds.)
In other words, we are made out of the most common available materials (discounting helium which doesn't react with anything so doesn't produce interesting chemistry), including the element that produces the most complex and varied chemistry. So if you are looking for complex chemistry (i.e. life) elsewhere in the galaxy, it actually does seem to be a reasonable starting point to expect that it is fairly likely to also be based on the most common elements available, and on the element that produces the most complex and diverse chemistry.