Apparatus and methods for use by a customer for trading assets, such as foreign exchange instruments, using a variety of trading protocols on an interconnected computer network, such as the Internet. The invention generates and displays easy-to-use, context-sensitive and meaningfully organized panels or windows containing visibly distinctive, user-activatible selectors and input controls the customer can manipulate to select and execute trades against the best available quotes as they are supplied by multiple providers. In a single-bank execution mode, the invention automatically determines the best quotes received from a multiplicity of providers and helps the customer submit a single-bank order to one of those providers. In a multi-bank execution mode, the invention automatically identifies and helps customers submit a best multi-bank order, which may comprise a combination single-bank orders split up among multiple providers who have each submitted quotes having insufficient sizes. The user also may specify other trading terms, such as trading accounts and order sizes, for the assets to be traded.