I believe the point GoNz0 is trying to make is as follows:
If you intend on running a game/web server at home, unless you are going to be investing in a dedicated symmetric high speed line then you are more likely to run into performance issues as a result of limited bandwidth and / or high latency connections rather than limited server hardware performance.
If you wish to host a few people on the server at any one time then you may well get away with it providing their latency to you is not too high. But many people will likely ruin the experience for everyone as residential ISP infrastructure is not designed for this use and thus multiple simultaneous connections will grind your internet connection to a halt. This will be an even bigger issue if you also plan to host web sites whilst you are hosting a gaming session.
You can avoid these problems by purchasing a dedicated high speed line, however these are not cheap! it will work out much cheaper for you to pay a hosting company for a dedicated server as they will provide the high speed and low latency network connectivity and you can still manage your server remotely (and have someone to phone/email if you need assistance). But this all depends on how serious you plan to be with this.
I suggest you do some research on the web and find some forums/websites where people do this sort of thing, that way they will be able to give you a good idea of what sort of server specification and network infrastructure required to do this effectively.
Either way good luck, hope it goes well.
Nemz.