@Smorath Bare, bare minimum? Single core 1990's Celeron, a 500MB PATA Disk.
There is really no minimum, I mine with my phone and 120GB of storage. If you want to mine a lot of disk, you'll need to make sure you system is effective, but anything can mine - there are people mining on Raspberry PI's.
If you want to go to the other extreme, my current build has 4 x 8 core/16 thread Xeon CPUs, 128GB RAM and 192TB of storage.
It's all about matching your system to your capacity.