On Mario party 3 all you need to do is choose the blue star and choose characters choose a board map and your on your way. If you want to play minigames choose the yellow star, duel map? choose the red star.
I've heard that Mario party 4(gamecube) is the best (i haven't played it though) B. I think it's Mario Party 2. ( I wrote B. because I'm a different person.)
It really depends on what type of birthday party. If it's one for adults, then check out thezencapitalist.com. They have an article called "The Best Party Games on the Cheap". It's definitely worth...