If you've got a sensible ISP, you can host from home just fine. You'll need an ISP who can permit traffic on port 25 (usually blocked for domestic connections)

If you've got a sensible ISP, you can host from home just fine. You'll need an ISP who can permit traffic on port 25 (usually blocked for domestic connections); a "static" IP address really is necessary (a fixed address, not behind a NAT); and your ISP must be able to handle your reverse DNS entries (IPv4 and IPv6). Any ISP who can handle commercial customers will be able to do all that. And a UPS power source is highly recommended. In some ways, email is a good place to start self hosting. It's based on store-and-forward, so you can be down for a while ... and when you come back up, any stored email will be delivered :) But be aware of security, and don't let your server become a spam relay!