Currently self-hosting a pi-hole instance, an nfs/smb server & a LAN-only webserver, as well as 24/7 syncthing (to which I automatically send my phone's photos to)
My specs are:
Intel Atom N270 (1 core, 2 threads)
1Gb DDR2 Ram (God knows the frequency but it's slow.)
And a 500gb HDD
You really don't need a lot of oomph to self host! I'm planning on running a qBitTorrent webui next.