Yes, a NAS (Network Attached Storage) is a great solution.
With desktops and laptops we've had good experiences with
www.synology.com but there are other ones that are just as good I'm sure.
The synology ones allow you to also
backup the NAS itself to the cloud (to different cloud providers).
So you could have your computer in one room, the NAS box hidden somewhere, the two them connected to your router (either by wire or wireless), then the NAS also backing up to the cloud.
It's a great solution, but for many it's probably a bit too complicated, and the cost of keeping the backups in the cloud soon start adding up. The Amazon Glacier is very cost effective if you don't mind waiting to get your backups back after a disaster - if you had a 1Tb (1000 Gb) then this works out at about £7 per month.
For most people, just backing up your computer onto an USB External Drive and putting it somewhere safe (preferably somewhere away from home) is cheap and simple. You just have to accept that when you do need it, then there's a good chance you won't have backup up for a while so you'll just lost that bit of data.
If you don't have much data, you don't need a big external hard drive. Nowadays it's more future proof to not buy one much bigger than you need, because the costs of storage keep tumbling and the technology keeps moving on.
It's just what works for you, really.
Trystan