I'm running my instance on 2 cores, 2GB of RAM. Of course I'm the only one on there at the moment, but it's running great, and I think it might even be fine with a single core.
As other have said, if you are planning to use it for your own "user's home instance," that should be fine. I've read a few people are running their instances on Raspberry PIs, which is pretty neat. While I have one I could use, I opted to setup a new droplet in DigitalOcean instead (I also run my own servers like you). A 2 core / 2GB RAM / 50GB SSD disk droplet on DigitalOcean is about $18 (USD) a month, while a single core droplet is about $12 (USD) per month.
If you plan to run an instance for others to use, be aware the federation is going to be chatty on your home network, and could impact other devices on your network. Probably not ideal, which is why I opted for a droplet in DigitalOcean instead.