In responding to your question, I will assume that you are interested mainly in the relative ranking of brokerage firms. In other words, your concern does not focus primarily on the merits of different types of accounts - such as individual versus business, regular versus retirement, and so on.
The best brokerage firm (as well as the best type of account) depends on your particular circumstances. Examples of relevant issues are the frequency of trading; the average size of individual trades; and so on.
Regardless of your needs, a great starting point is an annual survey conducted by a publication named Barron's. The most promising brokers are evaluated and also classified into different groups. A sample of the latter is the best set of brokers for long-term investors, or the top group of candidates for international trading.
The relative rankings of the brokerage firms do not vary much from one year to the next.
The results of a recent survey are presented in an article at the following address: http://online.barrons.com/article/SB12369873406242...
Please let me know if you have any comments or questions regarding this explanation.