There are many basic savings accounts available for you. The savings accounts, which are offered by most banks, are best for sinking funds and emergency funds. This is money that you want to have easily accessible to you. This means that you may sacrifice earning higher returns on the money, so you will not want to put all of your money into these types of accounts.
The first account is a basic savings account. You can open this account at any bank or credit union. The interest rate on a basic savings account is usually pretty low, but it should be higher than an interest earning checking account. Many banks limit the number of withdrawals you can have during a month, and most of these accounts have a minimum balance requirement before you start earning interest on the money.
A better savings account is a money market account. The minimum balances on money market account tend to be higher. This account should not be confused with a money market mutual funds account. A money market account should still be guaranteed up to $100,000, while a money market mutual funds account is not. You will still have a limited number of transactions per month, but your money is still fairly accessible. The interest rate on a money market account is variable, which allows you to earn more as the market is better.
A third type of savings account is a Certificate of Deposit (CD). The money in these accounts is not very liquid. You open up a CD for a set length of time usually between six months and five years. If you withdraw the money before that time you will incur a penalty, which is usually the interest earned up to that point. These are nice if you know that you will not need the money for a certain period of time. One difficulty is that you lock in the interest rate. If you lock it in at a low rate for a five-year term, you can end up not keeping even with inflation. But if you lock in with a high rate and the market drops, you can make a good return on your money.
You may want to open a variety of these accounts to best serve your needs. It is important to realize that you should use investment accounts for the majority of your wealth, because the rate of return on these products is generally not as good as you would get in a mutual fund. You do want to keep your emergency fund in a liquid (easily accessible) account though.