I'd again recommend a Raspberry Pi (ideally 4 with 4GB+ RAM), but with some modifications.

- You can choose an high endurance MicroSD card to maximize its life.

- You can delegate big file storage to something external (a HDD or SSD w/USB 3.0 connection). If you want something small, SanDisk Extreme Pro USB stick is a real SSD with USB-SATA bridge inside and 400MB/sec throughput.

- Armbian writes logs and swap to RAM in a compressed manner and will only commit logs back to disk during restart/shutdown. You can modify Raspbian to do the same I think. Armbian is not present for Raspberry Pi, my bad, sorry.

I'm using Armbian on a OrangePi Zero to run dnsmasq, qbittorrent (humble bundle downloads and ISOs), syncthing and other couple of services. I've delegated storage to an external USB 256GB drive and it's doing fine for now.

It's not as powerful to run Kodi and other multimedia stuff, but it's a plug and forget matchstick box which makes my life way easier.

To put the money where my mouth is:

1. A little how-to for storing your logs in RAM, a la Armbian style:

- https://github.com/azlux/log2ram (It's still updated)

2. Move your SWAP to ZRAM, again Armbian style:

- https://github.com/foundObjects/zram-swap

This two will improve your SD card life considerably.