You can use grocery store produce, however be aware that most produce is picked slightly underripe and often coolstored for long periods.. this can affect the flavour and amount of juice you will get from the fruit.
If using shopbought products.. I'd suggest you choose pre packaged juices for ferment.. It can often work out cheaper and you cut out a lot of work for yourself. If using juices.. read the back of the packaging carefully.. you want 100% juice ( not 'fruit drink') and 'no preservatives added'. Some preservatives.. such as potassium sorbate.. will make your fermentation difficult, if not impossible, to get started.
Allie