Florence is one of Europe's best cities for leather goods, paper products, and artisanal food. The leather market around San Lorenzo is mostly tourist-grade; for quality, look at the shops on Lungarno Corsini and in the Oltrarno. The bookbinders and paper-goods shops (Giulio Giannini & Son near Palazzo Pitti is the benchmark) sell marbled paper and leather-bound notebooks that are genuinely made in Florence.
Via Tornabuoni is the luxury shopping street — Gucci, Ferragamo (whose museum is at No. 2), Prada. The Officina Profumo-Farmaceutica di Santa Maria Novella on Via della Scala is the most distinctive shopping experience in the city.
For food, the Mercato Centrale (ground floor) has the best ingredients: olive oils, aged balsamic, local cheeses, truffle products. The Sant'Ambrogio market further east is less touristy and cheaper.