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First off if you're going to host from your home ISP connection it probably is against their TOS to run servers from your connection. Some ISPs block access to different ports. Secondly you will need your ISP to help point DNS stuff to you aknowledging your going to be doing something fun ;)
Secondly if your computer goes offline its down. No fingers to point at people -- if its for personal sites then sure there isn't much loss if you don't put much value on the site. Most hosting facilities have tens of thousands of dollars worth of hardware keeping servers online, backed up with power and cooled properly, something a low monthly rate can justify ;)
If you want to learn from more of a sys admin point of view go for it, put up the servers figure out what you need to make the sites accessable and security of the server (requires more than a firewall, needs manpower to apply fixes, upgrades and updates.)
My first servers were home run until the ISP enforced the no hosting rules, they were only accessable via IP address also, which changed since I wasnt on a static IP address.