Yeah, is it important to have a REALLY strong internet connection at the begining?
This is not something you want to host out of your home or small office. If that of course is what you are thinking.
Unless you have the following.
Redundant fiber connectivity.
It's best to start with a Reseller, VPS or Dedicated box (in that order) maybe colocation if you have your own gear. Something preferably on a 100Mbps link, but starting out would probably be fine on 10Mbps.
you need good upload speeds - I have an upload speed of 1mbps currently at home and I won't dare host any of my popular sites - visitors will end up lagging after a point. I run gameservers at home which is fine and can handle up to 30-40 connections at the same time but it's not nearly as much as some websites get - you should also check with your ISP first, I hear some ISPs block port 80 unless you get a business package.