Answer to updated question (see below for original answer):
You'll actually be bound by gigabit networking limits before CPU or Disk in scenarios involving sequential I/O (like a media server with video, music, or photo files) and more than 1 disk. Random I/O will bottleneck you on platter disks, but SSDs will easily put the bottlenet back on the gigabit networking. Some platter disks can saturate a gigabit line by themselves (WD Black drives, 10K rpm drives, 15K RPM drives)
For reference, using 5 disks I can easily hit more than three times gigabit speed with sustained sequential I/O. Using an SSD as a cache drive (with ZFS), I can fairly easily keep both gigabit lines on the server saturated for many (but not all) workloads.
More CPU / RAM comes into play when you want to start running applications on the NAS, such as a backup utility (i.e., CrashPlan), media transcoding/streaming or other CPU-intensive tasks that aren't related strictly to storing data on disk.
A NAS really is just a headless PC with less CPU/RAM, often with an embedded OS.
This question is far too broad to offer any real performance metrics, but know that it can matter. I recently purchased a small ARM-based NAS device, and found that the CPU couldn't handle all the calculations at full speed (RAID5 requires a respectable amount of CPU power). I was copying files at 30MB/s instead of 100MB/s (roughly gigabit speed).
This question is borderline off-topic because it's really broad, but it ultimately boils down to what you plan to do with the device. Most NASes are nice and self-contained; They boot and shut down quickly, have easy-to-replace drives, but are often make you choose between "expensive" or "slow". Desktops and servers are relatively cheap on the other hand, and you can do more with them, but you'll find yourself doing lots of setup yourself (installing the OS, configuring drives, etc.). I'm moving away from embedded NASes because I don't mind the configuration work, and I want to do more on my fileserver than I can reasonably do on the embedded NAS that I have, but that's a personal choice that nobody on this site can answer for you, and hardware changes far too fast for us to give out recommendations.