Or is the usb on the Arduino nano going to be enough to use as an input?
No, it probably won't... The USB in the Arduino is a virtual RS232 port and not a USB HOST host controller nor is it a USB HID interface. So really , the VDIP is the most logical/economical solution to adding a host controller to the Arduino... even if it's slow.
There is an FTDI product other than the VDIP1 that may be a way to get what you want. I would recommend you look at the FTDI VDRIVE2 or start fresh and look at the FTDI VMUSIC 2 as a peripherals to add to the Arduino.
VMUSIC2 obviously is an option only if you can use the PC to capture data to an MP3 file, then to a flash using a PC.
I would not expect the Arduino to be much help if what you want can't be done with a PC.