How much would, say, Botticelli's The Birth of Venus have cost the Medici family relative to the income of an average person at the time, and is it possible to approximate that cost in modern dollars?
The cost would've actually varied wildly by medium, artist, and the level of involvement of the artist. Baxandall's Painting and Experience in Fifteenth Century Italy collects some figures. Domenico Ghirlandaio was paid 115 florins for the Innocenti Altarpiece in 1488 and Fra Angelico 190 florins or "however much less he think proper" for another altarpiece, that of the Linen-weaver's guild, in 1433. Fillipino Lippi, working at Rome in about the same period, was paid 2,000 ducats but with his materials paid for separately(bear in mind that in most cases, the prices assumed that the artist would buy their own materials, which could be an expensive propostion). Boticelli himself as it turns out was paid 75 florins for his Bardi Altarpiece in 1484, with 35 florins of that specifically for his labor(the remainder was for pigment and the panel). In some cases artists could work on salary for princes, thus for example Andrea Mantegna worked on salary for Ludovico Gonzaga. A direct conversion to costs in modern dollars is probably unwise; as a more useful comparision is to the price of a day's labor as given in this tableEDIT: The link does not work, Goldthwaithe's The Economy of Renaissance Florence gives 70 florins at about the maximum annual salary of a skilled craftsman(that is to say, someone more or less about well-off enough to be respectable) and salaries in the city chancellery could range from 60-190 florins. So a painting like this would be quite an expensive undertaking.
I'll note, because it fascinated me, that prices and markets were quite distinct from city to city. painting, as a trade, was coming into its own at this period--and certainly not all at once across italy. based on relative affluence, level of education, social climate, etc., each city would have had its own relationship with its artistic community.
For example, Rome may have had the money and cut-throat, reputation-driven patronage system associated with the time period, but in 17th century Naples you'd have found a market teeming with middling 'factory painters' (my term) whose livelihood, based on the inundation of other uneducated (Naples had no proper art academy and lost many of its artists to a plague) painters in the local market, was dependent on the salaries they'd get by toiling away in the workshops. Copying and especially reselling others' work (names really didn't mean much!) would have been the main pursuit of Naples' painters. Foreign collectors wouldn't bat an eye at Neapolitan art, and foreign talent cornered the market of affluent patrons, so Neapolitan painters, by and large, made paintings as cheap commodities.
Even the 'big' commissions wouldn't have made careers, too: the price ceiling in Naples was ~300 ducats, even for stuff by the best in the city (Giordano, Stanzione). In fact, Giordano's 'business model' wasn't to milk patrons and inflate prices because of his reknown but rather to just take and collaborate on literally thousands of commissions. They didn't call him "fa presto" for nothin'.
Source: Sohm, Phillip. Painting for Profit.
From Ernst H. Gombrich On the Renaissance, Norm and Form p. 52: "The valuations attached to precious tableware and stones in the inventory of the Medici collection must indeed make one pause. The scribe or notary who drew up this inventory may not have been a great expert, but he must have known the correct order of magnitude. He valued the engraved gems of the Medici collection at betewen 400 and 1,000 florins each, the Tazza Farnese even at 10,000 fl. Now the average painting by a master of the rank of Filippino Lippi, Botticelli or Pollaiuolo would range between 50 and 100 florins, even a huge fresco cyle such as Ghirlandajo's Story of St. John in Santa Maria Novella only cost about 1,000 florins."
Gombrich himself cites as his source Wackernagel's Der Lebensraum des Künstlers in der florentinischen Renaissance (Leipzig, 1938) p. 346