As I am planning to go to Italy for business purpose for 6 days, then I am planning to travel other European countries too for next 10 days, which kind of category (business or tourism), should I choose, while applying for visa?
There are not different categories of Schengen short-stay visas -- there's just a single kind, which once issued is valid for both business and tourism purposes.
The visa application form will ask you for the main purpose(s) of your journey, and you should answer that truthfully. From your short description it sounds like the business in Italy is your main purpose for traveling -- even if you're choosing to combine it with some touristing when you're in Europe anyway, and even if this incidental touristing will last for more days than your main business purpose.
On the other hand, if going tourist and doing business are equally important for you, simply check both boxes. It does say "purpose(s)", after all.