To what artistic/cultural enterprises would the wealthy most likely contribute today if they had the resources and the power of the Medici family?
This is a good question. I would start by saying that the wealthy do actually support the arts in many ways. So, all we need to do is look at what is being done now.
For one thing, many wealthy people believe in public art. So, rather than collecting art for themselves, they donate large sums of money and art work to museums. Some of the money goes to getting art to display and some of the money is used to have special exhibitions for people to enjoy and appreciate.
Another way the wealthy support the art is they put up art work by commissioning artists to beautify our cities and towns. For example, in the city that I live there are many installations all over the place in public areas. The weatlhy have done this.
Finally, the wealthy also donate money to schools and art centers to keep the arts alive.
During the Italian Renaissance, rich and powerful families like the Medici in Tuscany, the Borghese in Rome and so on, were also patrons of arts and artists, and men and women of culture, refinement and aesthetic discernment-- protectors and commissioners of many artists and their works that have come down to us today, and that represent significant parts of human artistic/cultural heritage, being the fruits of their support. The likes of Michaelangelo, Raphael, D Vinci and others, owe them much.
Yet, it would be unfair to say that the rich and powerful today, in various parts of the world, do not provide support/patronage to the arts, especially in the West and developed parts; and in particular in the USA, where artistic and cultural endowments by the rich have played a very important part, too, during the 19th and 20th centuries, in helping promote arts and artists.
There seems to me to be very little change in the likes and tastes of such wealthy folk, from the Renaissance to this day. Back then, they mostly patronised painting, sculpture, architecture; and some music. Today, in the USA for example, they spend quite some money on paintings (mostly as investment), architecture/design and on leisure-linked music such as opera, orchestral music and so on.
Even major governmental initiatives/endowments, such as the NEA (National Endowment for Arts) today, owe a lot to such wealthy folk, in the early inceptionary stages. Most of the lobbying in the US Senate for its establishment, for example, in 1965, was by rich patrons of the arts. However, it would also be fair to say that the very rich at this present time (2012) are perhaps not so liberal in their support as they were in the early and middle 20th century, like the Vanderbilts, Guggenheims, Astors and so on.