How about a Goldeen? ( http://pokemondb.net/pokedex/goldeen )
1.) Its Little Cup
2.) Good attack stat for it (Best for that manner)
3.) If you have Lightning Rod ability, it only has Grass weakness, and thats canceled out by using a ice move like Ice Beam
4.) Its obviously it's not a legendary.
But, this is just one of the many pokemon that follows this listings. But, unlike the (supposedly) king of rain, Josh (Or TooJosh4U (But I would've spelled it 2Josh4U)), I'm not that bright in choosing weather teams, especially rain teams. But, I hope this works out for you!