The results achieved by William S. do not guarantee that you will achieve the same results. Being abroad, I do not have access to US telephone books, so I searched the Internet and looked at a rather large number of brokers' web sites. I also wanted to place orders through my PC, which would suggest that the broker has to be on the Internet. The brokers that satisfied my below criteria made it onto my shortlist. I did not consider brokers who are running a very slow site.
Some brokers only trade on one exchange, which is a bit too restrictive.
Full range of order types. Some brokers do not support limits very efficiently. Not offered by every broker. That you offer two types of access is absolutely ideal, in case one method fails. Initially, I thought that Internet access was the thing to go for, but I now prefer Wall Street Access for Windows.