If you have an always-on internet connection like DSL or Cable and a PC you can leave on 24/7 you can run it from home. Otherwise a VPS (Virtual Private Server) or Dedicated Server is highly recommended.
Due to the advanced nature of the bot shell/IRCd hosting services often don't have the libraries needed and may or may not install them. Also if you plan on using AutoDJ it will use more CPU power than an eggdrop or other bot and the shell company may not like that.
For tips on picking out a VPS or dedicated server, click here.