If you're considering the advantages and disadvantages of putting your cash away in a money market deposit account, then the best thing to compare it to is a savings account.
The main difference between a money market deposit account (MMDA) and your bank's generic savings account is that the interest rate changes on a weekly basis with a money market account (see Resources). Other than that, they are very similar.
Because money market accounts are based on the current market rate of interest, which can be found on most personal finance websites, the rate of return is typically higher than a savings account whose rate will not vary at all.
In addition to higher rates, you will also have similar access to your money as with a savings account. This means that you will be able to write checks and withdraw money.
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If you anticipate needing a healthy portion of your savings at any time, however, don't go with the money market account. They can sometimes require you to maintain a higher balance than your savings account, and will penalize you if it drops below the minimum.
If you need to withdraw money often, go with a checking account. Money market accounts will generally only allow you to write checks a few times per month. Just remember, the more money you take out of a savings account, the less compound interest you're going get.
Once you feel comfortable with the money market account, start looking into certificates of deposits and mutual funds. Investment-wise, they are the next step up from a money market account, and could possibly pay more interest.