One of the first things you should do is find out if your ISP blocks the incoming ports you need for whatever servers you want to run. Most do. Almost all prohibit usage of servers in their ToS unless you have a "business class" package. The other issue is simply how much upstream bandwidth you have and how reliable your internet connection is.

Running a server at home is great if you actually want to learn the ins and outs of administrating. I've always felt like there are three ways to administrate a server:

1) Just make it work. All sorts of problems lurking under the surface but it does basically what you need it to do until you find out one day something is broken and you have absolutely no clue how to fix it so you have an emergency Google session trying to figure out what a cryptic error message means.

2) Make it work well and follow some basic 'best practices' This is only as good as the HOWTO you're following. Definitely better than #1 but a much bigger hassle. Not as much of a hassle as..

3) Do it right. Learn the platform inside out. Fine tune everything. Develop rigid backup & maintenance policies. Keep current with security issues. Check your logs religiously. Maximize your uptime.

These are all perfectly valid approaches to it depending how important the server is but they all do include an element of hassle and upkeep versus paying someone a few bucks a month to do it for you.