If you are going to run a low traffic site (I consider a typical small biz website low traffic), a business DSL or cable connection will do the job just fine. Don't worry about redundancy too much, you'll probably find your network uptime is greater than most budget DCs can provide - just backup offsite and be happy. [My Biz DSL line in Calgary has been rock solid for nearly 4 years, and I often use one of my local FreeBSD machines as a failover when my leased dedicated server goes down].
You should consider using a separate machine from your regular home PC - you can pick up an old PII for next to nothing, FreeBSD will run like a dream on something like that. You'll probably be wanting a static IP address, and it's worth asking your ISP if they allow custom PTR records, or even delegate reverse DNS to one of your servers.
Last (but by no means least), you'll need sysadmin skills to manage your chosen operating system - good books are your best bet, supplemented by mailing lists, newsgroups and websites.