If you want to take in a complete summary of Florentine painting of the 1300s, all you have to do is go to the chapels at the back of the basilica, which conserve fresco cycle altarpieces and tomb sculptures of amazing quality: this is thanks to the basilica's patronage, but also to the rivalry of the city's major families, who always wanted to have the most beautiful works.
I suggest starting with the frescoes on the central vault behind the main altar, which depict the complicated and legendary events of the wood Crucifix the basilica is dedicated to.
Despite the imperfect conservation of the frescoes, you also have to see Bardi Chapel and Peruzzi Chapel, which were built for two families of wealthy financiers of the 1300s. In both chapels you can immerse yourself in the wonderful frescoes of Giotto, the most fundamental artist in the turning point of Italian and European art in the early 1300s.
In the climax of Franciscan religiosity that invited people to live with simplicity by loving nature and imagining the scenes of the life of Jesus and the saints as if they lived in the present, Giotto abandoned medieval traditions and painted figures, architecture, and scenes that directly reflected the reality of his time. The frescoes of Santa Croce were a fundamental model in the history of Florentine painting, and the great Tuscan artists like Masaccio and Michelangelo practiced copying them, fascinated by the powerful corporeity of their figures.
In Bardi Chapel you can admire the Stories of John the Evangelist; in Peruzzi Chapel, The Essential Moments of the Life of St. Francis. These two pictorial cycles painted by Giotto in the most mature and refined stage of his life are among the greatest masterpieces of European painting of the 1300s. Unfortunately, as you will see, the works have been damaged by lime and poor restoration works.
If you still want to see more Giotto, the painting on the altar of the Baroncelli Chapel is also his, even though it was entirely frescoed by his student Taddeo Gaddi.
At the back of the church you'll find a precious portal and corridor with beautiful carved doors that lead you to the great thirteenth-century sacristy, which is also coated with frescoes of the time. In the attached Rinuccini Chapel you can see realistic and well-preserved scenes of the life of Mary and Magdalene in a painting by the Lombard Giovanni da Milano.
FUN FACT: Giotto's mastery has been the source of many stories, and I'll tell you one of them: as a boy, when he was one of Cimabue's student, he painted a fly on the nose of a painting depicting his master. Cimabue didn't realize it was a fly, and tried to squash it!