Best Bugs on the island:
Emperor Butterfly (2,500)
Miyama Stag - trees (1,000)
Saw Stag - trees (2,000)
Giant Stag - trees (10,000)
Rainbow Stag - trees (10,000)
Cyclommatus Stag - palms (8,000)
Golden Stag - palms (12,000)
Horned Dynastid - trees (1,350)
Horned Atlas - Palms (8,000)
Horned Elephant - Palms (8,000)
Horned Hercules - Palms (12,000)
Goliath Beetle - Palms (6,000)
Best Fish -
Surgeon fish (1,000)
Butterfly fish (1,000)
Napolenfish (10,000)
Barred Knifejaw (5,000)
Red Snapper (3,000)
Moray Eel (2,000)
Blue Marlin (10,000)
Giant Trevally (4,500)
Ray (3,000)
Ocean Sunfish - w/ Fin (4,000)
Hammerhead Shark - w/ Fin (8,000)
Shark - w/ Fin (15,000)
Saw Shark - w/ Fin (12,000)
Whale Shark - w/ Fin (13,000)
More info on what months/times of day is on this website.
http://www.ign.com/wikis/animal-crossing-new-leaf/fish
Good luck!