Basically there are two options on how you can record the BMPCC's video output: Either interally on SD Cards or via the HDMI output, which can be set-up in the cameras menu to output a “clean” signal, even when the cameras screen shows informational overlays. If you want to record the RAW signal, SD-Cards are your only option, since HDMI cannot transmit RAW Video at the moment.
Blackmagic has a list of certified SD-Cards that work with the BMPCC, as of August 2014:
The following SD cards are recommended for CinemaDNG RAW recording:
There might be a possibility that other Cards work as well - at least for ProRes recordings - but thats a matter of trial and error or getting a personal recommendation by someone who has succesfully used other cards in his / her BMPCC.
There are very high-end solid state recorders as well, so we will just list a few of the more common options people use with the bmpcc.