In pokemon emerald you can catch Raquaza before the pokemon league. you go to the sky piller after the disaster is resolved. you will need mach bike to get there plus it is advisable if you don't want use your master ball,you should have several lv.60 or pokemon plus a ton of ultra balls to do it. it may take several tries.

As for the league you should use raquaza for your main pokemon plus also have some lv50to60 back up pokemon and some revives and hyper potions. you should beat them before on your first try