Which Turbo Tax product if filing the standard deduction for fed but itemizing state taxes (for home office)?

Deluxe, Premier, or Self-Employed will handle this, but your state must allow you to do that.  Some states do, some states don't.  And TurboTax follows the applicable state law.  If you want to confirm that your state allows this treatment for income tax, please see your state's Department of Revenue website.  State Department of Revenue List