darkmetal, I can't believe nobody here has properly answered your question yet! While it's possible to mix and match in any order I'd strongly recommend the following:
Playing the FF7 game first is not an option. Like was said, you won't understand jack shit if you never played the game or have a very good idea what went on in it.
1. Obviously play FF7 first! (duh)
2. Watch Last Order. Why? Well it is basically a cool anime version of an optional flashback sequence that describes the events after the Nibelheim Incident but before the start of FF7 the game, featuring Zack and Cloud and how they got to Midgar.
3. Watch Advent Children. Advent Children takes place TWO years after the events of FF7 and while it's not needed to know what happened in Last Order to watch Advent Children it'd be best you know what happened with Zack and Cloud beforehand. If you can't remember who Zack is or the extent of his relationship with Cloud some references in Advent children won't be appreciated.
4. Play Dirge of Cerberus. This is set THREE years after FF7.
The order they were released in isn't a mistake guys, each obviously builds off the other
The game -> Last Order -> Advent Children -> Dirge