If you have rented a place with a kitchen through Airbnb, VRBO, etc., then you'll probably want to cook. Here are some things I've learned about cooking in a rental in Venice.
Rentals will provide basic cooking equipment. The one thing that you're certain not to get is a good chef's knife. So if you have one at home, bring it (not in carry-on luggage!) in a knife guard. I was surprised that my rental didn't provide a rotary cheese grater (only a box grater) or a decent vegetable peeler, but every rental is different. The pots will probably not be very heavy-duty, so you'll need to be careful about not burning sauces, by using moderate heat and stirring often. If you absolutely must buy professional cooking equipment while you're here, go to GRAL (CR off Strada Nova, M-Sa xNoon).
Every neighborhood in Venice has a supermarket or minimarket, branded DeSpar, Coop, CONAD, or CRAI. For a good selection, go to one of the larger outlets. The DeSpar Teatro Italia (CR) is the largest and also worth visiting just for the interior, an Art Deco movie theater. The nearby Coop (CR) also has a large selection.
Supermarkets are fine for staples.