The audio guide is the best - a scion of an old Roman/French family talks not only about the art but about growing up in the palazzo. I'm not usually a fan of audio guides, but this one is great. It's not a place to get in a bucket list of "famous" paintings, though they bill it a such with the mention of the Cravaggios and the Raphael.
The most famous painting there gets little mention (but a great installation) - Velasquez' portrait of Innocent X. This baroque pope haunts the entire collection, from a bust in one of the first rooms to portraits in oil and stone throughout. the Velazquez portrait had a profound effect on both artists (like Francis Bacon) and filmmakers (like Adrian Lyne and "Jacob's Ladder") By emphasizing psychological study over depiction of power, this portrait helped establish what we now think of as a fine-art portrait, and modern art as a whole.
The curation is idiosyncratic, and what we took away from our visit was as much a story of 18th and 19th century collectors as it was of the Renaissance and Baroque artists on display. While you're there, check out the restaurant. They provided the best lunch we had in Rome, served with impeccable style in the loggia in front of the main palace.