A decent VPS would be better than running a server over broadband and is likely to cost not a lot more than the electricity of the PC you would have running at home.
If you want to try it at home, you will need plenty of spares, a UPS (and maybe a generator) a fast internet connection (fast upload, not just download), with port 25 open, for email. A firewall router where you can add additional ACLs for your customers.
If you get any kind of DoS, let along DDoS, you are hard down.
Some of our biggest servers only average 30-40 Mb/s, so you will be surprised how much you could do on a home connection, but customers are hard won and easily lost, so ensure you have a good SLA with your provider. A residential contract won't cut it. Any customer down for a day will be looking to leave ASAP.