I'm building toward exactly this, so take it with that bias. The cheap tier works if you lower expectations. An N150 mini PC with 16GB runs small models through Ollama fine, but 8B models are slow on that class of chip, and you'll feel it on anything chat-shaped. Where it shines is async work: summarize this, tag that, answer when it's ready. For phone access I'd keep it LAN-only and use WireGuard or Tailscale to get home rather than opening a port.
Disclosure: I'm working on a small open-source home box that bundles local AI with offline Wikipedia and media. What would make you trust a box like that over a setup you built yourself?