1. Determine the type of brokerage account you need
What are your investment objectives? If you simply want to invest for a rainy day or for a certain relatively near-term goal, and don't necessarily want your money tied up until you retire, a traditional brokerage account is the way to go. These accounts don't have tax advantages -- you may have to pay tax on investment profits and dividends -- but you are free to withdraw your money whenever you'd like. For this reason, a traditional, or standard brokerage account is often referred to as a taxable brokerage account.
If you choose a traditional brokerage account, your broker will likely ask if you want a cash account or margin account. If you choose to apply for margin privileges, this basically means that you can borrow money to buy stocks, with the stocks in your portfolio serving as collateral. You'll pay interest on the borrowed money, and there are some inherent risks involved with investing on margin that you should be aware of.
On the other hand, if your goal is to save money for retirement, an individual retirement account (IRA) is the best bet. Traditional IRAs can get you tax deductions when you contribute to them, but you won't be able to use your money until you're 59-1/2. Contributions to Roth IRAs don't give you a tax benefit when you make them, but qualified Roth IRA withdrawals will be tax-free. Plus, you can withdraw Roth IRA contributions (but not your investment profits) whenever you want. Finally, if you're self-employed, there are some special options for you, such as a SIMPLE IRA, SEP-IRA, or individual 401(k). You can read through a more thorough guide to help you pick the best IRA as well.
It's also worth noting that many people choose to open multiple brokerage accounts -- such as a taxable account and an IRA, in order to keep their money in separate baskets.
2. Compare the costs and incentives
These days, virtually all of the major discount brokers offer commission-free stock trading. They may also offer you a discount to reward you for certain actions, such as transferring a large investment account from another broker.
That said, it's important to review each brokerage firm's fees, particularly if you plan on trading anything other than stocks (options, mutual funds, ETFs, bonds, etc.), as these often come with their own costs. For example, many brokers charge a commission in the range of $0.50 to $0.75 per options contract, so even if the broker doesn't charge a base commission, options trading won't exactly be free.
Finally, many brokers offer incentives in order to attract business, and you don't need to be a millionaire to take advantage of them. I'm not saying that a good incentive all by itself should sway your decision, but it's definitely a piece of the puzzle worth taking into consideration.