Off-the-shelf or DIY NAS?
Obvious considerations
If you decide to purchase off-the-shelf NAS, obviously, you would have no problems building a NAS. You get off-the-shelf, compact data storage.
If you plan to build a home server yourself, you would have to actually build it. Additionally, you may run into a problem of providing a proper cooling in a small case.
Off-the-shelf NAS vs. DIY server repairs
For insignificant failures, e.g. a disk failure, NAS is the best option. It is very simple - the LED corresponding to the failed disk turns red and that's it. In case of DIY server you need to mess around trying to physically identify the failed disk. The identification would be much easier if you label the disks while building a server, but nobody does this in home builds.
For complex repairs, if a NAS box itself fails or the RAID metadata gets damaged, you need to replace or repair a NAS under the warranty. Also, sometimes a manufacturer provides remote metadata recovery over the Internet (QNAP sometimes does this). However, full-blown data recovery is only feasible locally. With a DIY server you have to repair the server yourself. It is faster and often you can repair more complex failures without a data loss, if you are skilled enough in hardware and software you use.
Thus, if you can repair a server, choose a DIY server. Most likely, your server will better match your own needs than an off-the-shelf NAS. If not, the best option for you is to purchase off-the-shelf NAS.
Continue to NAS devices.