Handlebars: The bars should be at least as wide as your shoulders, and typically a little wider on flat bars. I recommend ergonomic grips with integrated bar-ends (or separate bar-ends), which offer a comfortable alternative position for climbing/accelerating and just cruising.

Tires: The 700 refers to the wheel diameter. the other numbers relate to the width of the tire (25, 28, 32) in millimeters. The stock tires are 700x40, so 40mm wide. I personally prefer wider tires as there is little demonstrable benefit to using skinny tires (they're not that much "faster"), particularly for commuting, but if you want skinnier tires, I'd say start with 28's or 32's - very common widths.
A couple of key considerations for commuting tires are puncture protection and ride quality - finding the right mix can be a challenge. The more expensive ($45-$50 and above) commuting tires will typically have better puncture protection than less expensive models, but part of what you are paying for (whether you want it or not) is a lighter weight/foldable kevlar bead instead of a rigid bead (the lip that locks into the rim).

Anyway, I think you'll like that bike - it looks fun!