Dixie - Sorry to put cold water on your desire to have a family coat of arms - I would be misaleading you if I didn't tell you otherwise. I assume that you have people in the States as we have over here who will sell you a very nice scroll with "your" family arms on it.
Personally I think it is acceptable to display the ancestral Anderton Arms - silver shackbolts on black - as the rootstock that the Andertons spang from. This is the Arms of the family that owned the village of Anderton in Lancashire that the name comes from and is classed as "extinct".
Now if you are descended from one of the Historical branmches such as Lostock or Euxton, you are descended from this Rootstock if you go far enough back. If not then you are descended from one of the many people who came from the village of Anderton and as such probably worked for them so you would have worn their colours on your livery.
Either way I think in this modern world it can serve as a token of the family ties that know not the fetters of national boundaries (if you will forgive the heraldic pun).