You don't need much processing power or RAM for WireGuard, also it doesn't have to be Raspberry (it can be cheaper alternatives, like Orange Pi, Banana Pi etc.).
I do recommend getting an SBC with Ethernet though, WiFi on these SBCs can be flakey.
Anyhow here is one of mine, Orange Pi Zero running WireGuard on Armbian OS.
It fully saturates the ISP it is hooked up to (sh!ty cable provider with only 60 Mb/s upload, though it is enough - streaming usually takes up ~15 Mb/s per client) and it is barely putting any load on the SBC.
That being said I bought my OPi Zeroes for 10$ back in the day, they are now 25$... It is 100 Mb/s ethernet, you can find SBCs with 1 Gb/s nowadays, which might be a good idea if the ISP at your parent's house offers more than 100 Mb/s upload. Also, OPi Zero is meant to be used as a headless device (no video output / GUI, just ssh and terminal) and since you are just starting out you might want something with HDMI output and running a Linux distro with a desktop environment (and a bit more RAM because of the DE).
Depending on your budget:
- 40$ : Orange Pi 3 LTS. HDMI output, Gigabit Ethernet, 2GB of RAM and it has 8GB of EMMC (enough for OS, eliminating the need for a good SD card).
- 100$: Orange Pi 5 (8GB of DDR4 version). Which is IMHO a total overkill for something like this, but hey if you want something even faster than Raspberry Pi 4B but want to pay the same or less (RPi 4B is out of stock and heavily scalped) then go for it. it doesn't have EMMC but it has an M.2 nvme slot, which is a fair bit more reliable than SD cards. There is also OPi 5B 8GB variant with 64GB of EMMC for 125$... but IMO if you are paying this much you might as well get an nvme and skip EMMC.
(prices from the official store of Shenzhen Xunlong Software on AliExpress , with shipping to my where I live. You can also find them on Amazon)
A few notes:
1) Make sure your power supply is adequate. Either buy the bundle (SBC + power adapter) or check how many amps it needs and use an appropriate power adapter (same or better yet - greater amp value), preferably from a reputable manufacturer (not a no-name 2$ phone charger).
Crappy power adapters can cause system hangs, reboots, and all kinds of weirdness. You don't want to troubleshoot that if the SBC needs to be online 24/7 at a remote location.
2) If you will be running the OS from an SD card then buy a "high endurance" one (typically used for IP and dash cams), pick at least UHS 1 speed (guaranteed 10 MB/s sequential writes), or better yet UHS 3 (30 MB/s seq). 32GB is plenty of capacity.
Crappy SD cards can die quickly, not uncommon for them to fail in less than a year. High endurance ones from known brands (like SanDisk or Kingston etc.) easily last 2+ years.
It would be wise to clone the SD card to your PC once you've got everything setup. In case of a failure you can just burn that image to a new card and mail your parents the replacement.
3) You don't need a fan or an enclosure to cool the SBC, passive cooling for what you are doing is fine, so do get some heatsinks at least (2-3$).
PS my reply is growing a tad bit too big for this thread. If you need help setting it up start a new thread on the forums. I'll just add that with WireGuard you will most probably need to set up DDNS (because I doubt your parents have a static public IP, just how ISPs usually work), on your router you'll need to reserve a local IP for your SBC, and forward a port to the SBC.
