While the options mentioned above are possible, if you want local storage, a self build will work out a lot cheaper than an OTS solution, its not like most people here are afraid of spending 30 mins building a PC.
Synology and QNap generally make (over priced) off the shelf NAS/server boxes, you are tied to the for support lifecycles and sooner or later will find you either have a very expensive upgrade path or have to sell it and start again. Think carefully before going this route.
UnRAID - Cheap software that runs on your hardware, makes upgrades/using mixed drive sizes easy and you can build way, way better for a lot less than the equivalent multi drive Synology box will cost you and support is for life. You can mount could storage.
FreeNAS and its various derivatives - Free as the name suggests, similar to unraid but embraces ZFS which brings with it a few considerations in terms of hardware/drives, again you can mount cloud storage.
As has been suggested, depending on your ability and speed of connection, Gsuite Business does provide decent storage options, you can always combine it with a cheap linux VPS for a remote server/storage solution, run Plex on that and £700 buys you a lot of years of not worrying about power/heat/noise, drive failure etc.
As pointed out though, playback isn't straight forward, client choice, content type and connectivity need careful consideration along with server hardware. Give us the other parts of the puzzle and you'll get better advice (connection speed, technical ability, willingness to learn, need for local storage).
Power wise the difference is likely minimal unless you’re doing something CPU intensive, in which case it’s likely a self build for Synology money will significantly outperform a Synology, power gating being what it is, it’s back to idle and saving power. Offset it against the massive savings if you spec’d like for like? Not sure I follow the updates/management point, last time I fired up DSM I’m pretty sure I needed to manage updates/drives in a very similar way to UnRAID (eg click update), perhaps not so much in FreeNAS, but that would be down to my chosen file system set-up.
