Any bike will do. A practical, wet-weather utility bike will have fenders and a rear luggage rack, or at least the threaded eyelets on the frame to fit them.
If you fit a rack and get some pannier bags you can carry a lot of shopping on the bike, much more than you can carry.
The most common kind of basic bike is probably a "hybrid" style. Basic MTB is also good.
One upgrade to make is puncture-resistant tyres. The most common is Schwalbe Marathon, the best is Schwalbe Marathon Plus. They are not cheap but cyclists tend to get less leeway from bosses regarding late arrival than do their driving co-workers.

Useful accesories: Lock, lights, helmet, cycling mitts, trouser clips , spare inner tube, pump, tyre levers, wheel wrench, puncture kit, oil/lube.