Relevant clauses from multiple USA ISP's (scroll down a little) https://www.eff.org/deeplinks/2013/08/google-fiber-continues...
A typical data center will have multiple high-capacity backbones connecting their building to the internet which not only means better connections between your server and those connecting to it, but greater reliability and redundancy.
When you got port-80 working, you need some hardware: A cheap server and a cable to connect it to the router. An old laptop will do as server (KVM and UPS for free).
You also need to decide what software to run, I would go with Ubuntu server as it's the most friendly. Create a bootable USB-stick.
Setup SSH so that you can access the server from your work-station/laptop.
Signup to a DNS service and point a domain name to your IP.
I have a a switch, servers plug into that. I have static IP's. I have UPS's and separate electrical service for this. I also have a few rack mount AC units.
Comcast -> PfSense box -> Servers. I run CentOS.
PS: I also watched that episode. Did you notice the cabinet with SUN x'd out?
With any volume of connections, your cheap residential router will fall over under the load. xDSL and cable are both asymmetrical, so you don't have much upload bandwidth, and cheap ISPs frequently have 'no servers' clauses in their terms of service. The reliability isn't great, either. A business xDSL or cable service will fix the terms of service issue, and possibly get you a more reliable service, but isn't going to do much for the upload bandwidth.
You could get a leased-line type connection, which these days are generally delivered as Ethernet over optical fibre or Ethernet-in-the-First-Mile, which is a VDSL-ish symmetrical service. That's going to cost at least an order of magnitude more than cable or xDSL, and unless your garage happens to be located in a business district, you'll probably also have to pay for them to dig up the street and extend the network to you.
With either of those routes, your garage won't have redundant connections to the Internet, won't have redundant power or cooling (does it even have cooling to begin with?), a staffed NOC, or all the other things which go with a proper datacentre.
Cloud and dedicated hosting is so cheap these days that for anything more than a hobby project, I wouldn't even consider running a server from home -- and it's very questionable, even for the hobby projects!
Not really, assuming what you are trying to do isn't being subverted by your ISP.
That being said, cloud hosting is a race to the bottom in terms of cost - I wouldn't host locally ever again.
Colocation is also pretty cheap (I've seen ~$30-40/mo 1U w/ capped gigabit connections/no real power constraints, locally)
Most of the clients I run into anymore that really want to host their own is because they are being told no by co-location facilities or other providers because of content or usage restrictions. The other's are generally security concerned, but maybe don't understand all the work and repeated work that goes into hosting a secure server/service on the Internet, between network security, firewall rules, server patching etc.
Not saying don't just make sure your reasons won't get vetoed by the ISP.