A trolling rod is nice to have, but for many years we just used a 100# test handline. Small lures with skirts work well.
Not much for shore fishing, you might get some small jacks and such. Tuna come into the bays in the evenings to feed so may have some luck fishing off the boat while it's at anchor.
You'll be far enough south that if you catch a small to mid sized Barracuda offshore you can eat it without worry. They are slimy and smelly when you first catch them, but filleted they are very mild and tasty.
If all else fails, fresh fish can be bought for 8 EC ($3) a pound at the square in Soufriere, the fish market in Kingstown and also at the fish market in Bequia.
When you stop at the Tobago Cays, Jean Claude, AKA Mr. Fabulous does the best lobster dinners, if you tell him Sammy from Skyelark recommended him you'll be treated like family.