Venice is not a place for department stores or shopping centres — there are none. What it has instead is a density of small independent shops and specialist traders, scattered through the calli and campi of all six sestieri.
The Rialto market is the best starting point: the daily fish and produce market on the San Polo bank gives way to a ring of small shops selling food, wine, and Venetian specialities. The streets east of the Rialto bridge, toward Campo San Bartolomio, hold most of the practical shops serving locals — hardware, pharmacies, the kind of thing that keeps a city running.
Glass is the obvious purchase. The best Murano glass comes from the island itself, where you can watch it being made in the furnaces. In Venice proper, quality varies enormously — the cheap imported glass filling the tourist shops near San Marco is not the same as the work of the historic Murano glassmakers. For masks, the same caveat applies: hand-made papier-mâché and leather masks made in Venice are a different object entirely from the mass-produced imports.
The area around Campo San Barnaba in Dorsoduro and the streets north of Campo Santa Margherita have a cluster of interesting small shops — antiques, vintage, art books, locally made goods. The Mercerie, the shopping street connecting Piazza San Marco to the Rialto, is the main commercial artery and carries a mix of jewellery, fashion, and souvenirs.