I interrupted my replying when there were 2 answers, just one hour ago and now... 11 replies!
So, sorry if my post is out of place, or some things were already said...
You said the max frequency is around 30kHz (don't know if it is the fastest "bitrate" or the highest analog bandwidth required).
To go whole hog, the minimum sampling should be at least 60kHz, let's assume 100kHz. To monitor 4 bits/sample it means 50kB/s, resulting in 1MB for 20 seconds and 1.5MB for 30 seconds. For such a sampling frequency, I think that also a PIC will do the job. At each cycle it has to read, store the nibble to the upper/lower nibble of the register, write to memory and increment the address. If a fast PIC is choosen, running at 48MHz it will do 12MIPS, so there could be 12M/100k = 120 instructions/sampling period.
Memory becomes the issue, since MCUs are usually not equipped with that amount of memory. Even if a non-volatile memory would be better (SD card, for example), one easy way could be to use an external (parallel) RAM, and to maintain the board under a backup battery supply.
Then, an USB or RS-232 interface to PC will do the rest.