All three have their merits.
Botany has logs, seeds for gardening that sell fast. Mining has ore, soil for gardening. Fishing has, well, fish.

However, fishing does not have 'unspoiled nodes' nor can you gather shards/crystals/clusters. Miner and botanist get the special nodes that let's them gather certain special items like grade 3 Thanalan/Shroud/La Noscean soil and so on.
If you level both, you can follow the 'cycle of gil' as some people I know call it. Meaning, you just go from node to node to node.