You have to have a second FM Pro license in order to share desktop-to-desktop. You could have it running on one desktop and use FM Go as the client access, but it only works on iPad (or iPhone, of course).
For simply using an existing database, there are no advantages to using FileMaker Pro Advanced instead of FileMaker Pro. The only features in Advanced that are not present in FileMaker Pro are database design tools intended to help you modify the design of a database. So there is no reason to spend the extra dollars on FileMaker Advanced to install it on a client machine unless you plan to use that client machine to create or modify databases.
Note that custom functions and custom menus added to a file by Advanced work just fine when the file is opened with FileMaker Pro. You just can't change them with FileMaker Pro.