Yes, I have a one computer to perform a multitude of server functions for my home.
For your purposes any dual core computer with 8gb of ram from this decade will be just fine.
In regards to being a NAS:
You can just hook up a bunch of drives and share them individually, or you can use the motherboards built in RAID utility, or you can get an aftermarket raid card. Most motherboards built in support for RAID0/1/10 is adaquete but most are not up to the task of handling parity for RAID 5 or 6 so you would need a dedicated raid card.