Internal memory and µSDXC reader r/w support
The Note 3 has 32 GB or 64 GB of internal flash memory, that can be increased by adding a µSDXC card. While so far the max. available size is 64 GB, any SDXC reader conforming to specs should be able to read up to 2 TB. The largest SDXC card available is 256 GB, which already already worked in the Note as can be read at [c].
External USB HDD, USB flash drive and USB SD/CF reader r/w access
But there is a cheaper way to extend external storage, since Samsung does not require root rights to have r/w access to memory connected via an USB OTG cable, you can extend the internal memory as needed. While the USB port provides enough power to drive also an HDD I do not recommend it due the constant current of >=0.5 A drawn by most HDD.
USB flash drives require less power and even newer USB 2.0 flash drives are fast enough to enjoy watching films.
USB SD or CF reader allow also access, however due to unnecessary current draw I would not recommend to think about using your old CF-µDrives.
Memory access via WLAN
While due to the r/w support to memory via USB OTG cable not necessary, it should be possible to use also storage via WLAN or NAS in the router, but I have not tested it so far.