Yeah, don't try a home operation unless you can afford to get everything that you'll need. You'll need some redundancy even if it's from home, something like an extra line with the same capacity, generator(s), and more. If your starting out a data center would be the best choice.
Depends on where you live. It shouldn't be too expensive if you're in a large city. You might want to start out on a managed server to get the hang of things; that will be cheaper than buying a quarter-rack of colo space.
From the postings I see on the dedicated servers section, it is really cheap to just get a dedicated server and start hosting, no point tolerating the downtimes and slow speed of a 1mbps broadband, really cant host much with that