It's hard to say if growing your own fruits and vegetables in general would save you a lot of money because you will need to spend money on the supplies, soil etc. to grow your food. However, you will probably save compared to buying organic fruits and vegetables plus you'll have control of what goes into growing them. If you never had your own garden, try starting with the easy stuff. For me cherry tomatoes, lettuce, italian or chinese parsley and bok choy (a type of chinese cabbage) were easy to grow and delicious.