There are dozens of types of berries: blackberries, raspberries, strawberries, blueberries, cranberries, red currents, etc, etc. Each one has its own flavour and each one will add its own taste to the smoothie.
One thing to watch – some of them can be quite tart. For example: red currents, cranberries and lingonberries. These are best mixed with their sweeter compatriots to ensure that the resultant mixture is well balanced. This is down to personal taste – I happen to like the sourness of the red current and leave them well alone. Your mileage will vary.
I often buy my berries frozen, as they are then available all year round. This also cools the smoothie down – which often helps with the taste. Look for berries that are frozen without any added sugar or syrup.
Pre-frozen berries are not normally as tasty as fresh ones you then freeze yourself. So, at peak season I will buy large quantities of berries quite cheaply – then freeze them. You do need a large freezer to do this however.