Adam,
The "full" version of SQL 2005 is just that. The full version: SQL Server 2005. It comes with SBS 2003 Premium Edition and other server OS. If not, you have to pay for it as it is Microsoft's actual flagship database. SQL Express is Microsoft's free version where My SQL is an open source Sequel database.
SQL Express would install completely to the "main computer" and be the database for AC whether SQL Server 2005 was there. If SQL Server 2005 is there as it is on your computer, then the AC installs SQL Server Express as its own "instance" which are basically separate installs of SQL within SQL Server 2005. It was designed to install this way and so I would install it that way. Some try all sorts of different methods on here and, for some, they have their reasons. I see little reason to do so.
As to the clients, there is no need to install SQL server and you should not. There is the screen, which comes up that asks you if you are going to be using the client as the main computer. That is where you select the second option. While it will work that way, I would recommend uninstalling SQL off any client as it will take up resources and there is actually no reason for it to be there.
