Just my take on this having brought my fisher to level cap. Basically grinded to 51 and then used blue scrip collectibles to level through to 60. Basically a combination of the information you can find here and here.
1-5
Limsa Lominsa Lower Decks | Lugworm
5-10
Murmur Rills (North Shroud) | Crayfish Ball
10-15
Swiftperch (Western La Noscea) | Goby Ball
15-20
Fallgourd Float (North Shroud) | Midge Basket
20-23
Oakwood (Upper La Noscea) | Crow Fly
23-27
The Burning Wall (Eastern Thanalan) | Chocobo Fly
27-30
Ceruleum Field (Northern Thanalan) | Chocobo Fly
30-35
Ceruleum Field (Northern Thanalan) | Sylphid Basket
35-37
Sagolii Desert (Southern Thanalan) | Sand Leech
37-40
The Nail (Coerthas Central Highlands) | Wildfowl Fly/Honey Worm
40-44
The Burning Wall (Eastern Thanalan) | Stem Borer
44-45
Exploratory Ice Hole (Coerthas Central Highlands) | Topwater Frog
45 - 50
North Silvertear (Mor Dhona) | Glowworm
1-5
Limsa Lominsa Lower Decks | Lugworm
5-10
Murmur Rills (North Shroud) | Crayfish Ball
10-15
Swiftperch (Western La Noscea) | Goby Ball
15-20
Fallgourd Float (North Shroud) | Midge Basket
20-23
Oakwood (Upper La Noscea) | Crow Fly
23-27
The Burning Wall (Eastern Thanalan) | Chocobo Fly
27-30
Ceruleum Field (Northern Thanalan) | Chocobo Fly
30-35
Ceruleum Field (Northern Thanalan) | Sylphid Basket
35-37
Sagolii Desert (Southern Thanalan) | Sand Leech
37-40
The Nail (Coerthas Central Highlands) | Wildfowl Fly/Honey Worm
40-44
The Burning Wall (Eastern Thanalan) | Stem Borer
44-45
Exploratory Ice Hole (Coerthas Central Highlands) | Topwater Frog
45 - 50
North Silvertear (Mor Dhona) | Glowworm