Carry one spare inner. Keep another stashed at work. Practice changing tubes in comfort.
Consider some backup LED lights, mine are tiny watch battery style with elastic fittings.
Sufficient tools to adjust seatpost, saddle, bars, rear mech, brake/gear cables. Small blade for picking out glass. Leatherman small pliers are always handy. Chaintool is only useful if you can use it, I've never needed it for commuting.
Make sure your tyres are of sufficient quality with good puncture protection.
Rear rack and panniers are useful, one pannier is sufficient for a commute.
Keep your repair kit in a small bag in your pannier. Under-saddle bags are good for training and day rides.