Once upon a time, discount brokerages did not offer mutual funds as an investment alternative -- but times have changed. However, the selection of mutual funds can vary widely from broker to broker. If you're set on using a particular mutual fund family, make sure the brokerage you're selecting offers that family of funds.
You can buy no-load mutual funds directly from mutual fund companies, so unless you're a mutual-fund trading addict, the availability of thousands of mutual funds in one location probably shouldn't affect which broker you choose. While you can purchase some no-load mutual funds from discount brokers without paying a transaction fee, some brokers do charge a fee even for no-load funds -- so be sure to check on this before making a purchase.
Beyond equity mutual funds, there are a number of other investment vehicles that you may wish to use. All brokerages will offer the stocks traded on the major exchanges. However, if you're interested in risking your hard-earned moolah on over-the-counter (OTC) bulletin-board stocks, you'll have to see which brokerages offer them.
Other choices -- such as options, government bonds, corporate bonds, stocks traded on foreign exchanges, and the like -- aren't always available from every broker. Determine what you expect you'll need (we're fans of just plain old stocks, especially if you're young!) and choose your broker accordingly.