The 4204 will end up giving you a real bad time since the pi doesn't have enough i2s inputs to support it, and it has a ton of pins.
The 1804 and 4202 both cannot operate without an external clock, so it needs something like a crystal, or other source of SCK supplied to it.
My suggestion would be that you look at the PCM186x series. These have PLLs and can generate their own master clock from the input BIT CLOCK in slave mode (in master mode, you need to supply it with a crystal or an SCK), so you can build a circuit for one of these with nothing more than a few capacitors. More specifically, you could do a PCM186x with as few as 1 capacitor, plus 1 additional on each analog input channel (8 in total), although it would generally be recommended to add some to the supply lines as well. They can also mix/mux signals, and in the case of the 1864/5, can output 4 channels in TDM mode, so they can supply the pi with 4 channel audio with just 1 audio signal wire. The PCM1862-1865 are software controlled over i2c or SPI, and there are drivers for them in the kernel.