Consider your own requirements ahead of the headline interest rate
Can you truly afford to lock away the money you want to save for a long time, and are you sure you won't need access to it suddenly?
Any of the very best savings plans, in terms of interest paid, almost always involve locking away your money where you won't be able to get to it in a hurry. For example, a savings plan I was reading about recently when I was looking to invest a couple thousand required that you give SIX MONTHS notice if you wanted to withdraw ANY money without incuring a penalty! This is fine, of course, if the money you want to save is truly in the zone where you can leave it alone for that period of time, but, for most of us, the thought of not being to access what is, after all, OUR money, easily does not sit well!
On the other hand, instant access savings accounts, where your money is not tied up at all, such as those likely offered by your current banking institution, often offer a measly interest rate -- and remember that you will have to pay tax on standard savings accounts, too!
!! TOP TIP: Before you think about saving money in a savings account or making an investment !!
Pay your debts off first! (I'm making a possble exception for your mortgage, if you have a low interest rate - you need to check!)
In any financial climate, and in order to make money, bankers will always charge more to borrow money than they will pay on interest (at least in a standard savings account). So, if you have any debts, and these debts are not "soft loans" from family or friends, or limited 0% credit cards debts that you fully intend to pay off anyway, then you will always save more money by paying off the debts before stashing the cash!
However, if you are offered an excellent interest rate on your savings, always check the ramifications and penalties that may apply if you withdraw your money quickly (too soon for the terms), and check that you are comfortable with it before you proceed is a key piece of advice I want to give to you.