An easy out of the box solution would be a synology NAS.

For HW I personally use a NUC. If I were to build something today within said budget, I’d go for a second hand thin client.

For example the Thinkcentre M720q Tiny I can buy for 225EUR, coming with 8th gen core i5, 8GiB RAM, 256GiB SSD (1). Idle consumption is around 5W.

I use syncthing to sync folders between phone, tablet, desktop and my home server (a NUC).

Then rsync on a schedule from the server to a second off-site server (also a NUC) as backup, connected through zerotier.

I know of truenas, which is a more NAS like solution, but haven’t personally used that.

I use Feedbro, a firefox addon