I would like to plant a small garden for my wife
Gardening is the practice of growing and cultivating plants, sometimes referred to as horticulture.
Is there any limit to the types of plants that can be cultivated?
not at all! any plant cultivation is considered gardening, and it is also considered by many to be a relaxing activity.
Can i plant flowers and vegetables at the same time? 
Of course you can, people like to specialize though, some plants need special types of soil and fertilizers. It makes it harder to grow large number of different plants.
Is the history of the first garden recorded?
There is no way to know, we have been doing it forever! Forest gardens originated in prehistoric times.