I've only ever had one NAS so I'm not an expert -- a Synology DS413 with 4x2TB WD Reds in RAID 5. I can connect to it from the internet and have created user accounts for my friends to use the space. There is a huge amount of functionality there that I know very little about so it might be more useful for more experienced users. It can host a few programs such as media libraries, uMurmur, anti-virus, and lots of other things I know nothing about. The NAS and HDDs cost me about 800 euro in total.
My main problem is that downloading files from it across the internet is restricted by my ISP's upload speed (about 6 Mbps upload versus 120 Mbps download speed) which makes internet transfers painfully slow.
The HDDs go into power-saving mode when they haven't been used for 20 minutes, I have the fan mode set to quiet and have disabled all notification beeps.
It cost a bit of money and a newer 2-bay model might be just as good for my needs but I'm still happy with it. The DSM software (the same software on all models) is the big draw with the Synology models.
I also have a WD HD TV Live Media player connected to it over the router, which is very handy. But I'm sure there are better solutions these days for watching media. I have no HDDs in my PC (just SSD for the OS) so all my devices (PC, laptop, phone, tablet) can use the NAS for storage.
Edit: How come the comments can't handle the Euro symbol? Pressing AltGr 4 does the Euro symbol on my keyboard but after posting it, it just shows as "?"