While the ST32F407 claims Ethernet connectivity, it doesn't actually have the Ethernet transceivers needed to talk directly to a piece of network cable. This interface, commonly referred to as a PHY, is left to the user to implement. It appears that Ethernet PHYs have a few standard interfaces: Media Independent Interface (MII), and Reduced Media Independent Interface (RMII). A few key differences between MII and RMII include a reduced pin count for RMII, and the data clock rate is 50MHz for RMII while only 25MHz for MII. While I don't feel like I'm in a crunch for pins, the RMII I/O looks better due to fewer apparent edge cases that the MII interface supports. Browsing through available Ethernet PHYs, it appears that Microchip makes the least expensive versions, and the cheapest one (LAN8720A) only supports RMII. Since my research has shown a slight preference to the RMII configuration, I have chosen the LAN8720A to be the Ethernet PHY IC.
Another thing to keep in mind when heading towards an Ethernet-based device is that the selection of the jack is important. Looking for something straightforward, it's easiest to use jacks with integrated magnetics. This means that there are transformers inside the jack for each TX and RX pair used. The transformer windings for Power over Ethernet (PoE) are also different, as the cable side requires a center tap for accessing the DC power without disturbing the signal. There are a whole lot of flavors of jacks and PoE varieties, but ones rated for PoE+ should tolerate the highest amount of current.
Both the jack and PHY will be integrated into a daughterboard for the STM32F4 Discovery development board.