Well one of the first things I can tell you to consider is...are you just going to hunt the dry sand...or do you expect to go down to the wet sand.
We ask that for a simple reason. Most good metal detectors will do just fine up in the dry sand ( although some exceptions abound but usually on black sand beaches)...anyway once you get down to the damp sand things can change a bit as the salt water is conductive and can interfere with the detectors ability ground balance out the signal from the wets salt.
One item tI have to mention is..."not drop alot of money is subjective". Some detectors run in the $1300-1800 range so by comparison $500.00 is reasonable. However reasonable to you may be $250.00.....so best to state a price range and you will receive good input.
Myself...i would find a good used Fisher Gold Bug Pro around $450.00 and go with that. Yould never need to get another machine on the beach unless you went into the water and then that is a whole new story. the Gold Bug Pro is designed around detecting small gold and that is what you are after....unless you have a morbid desire for clad coins...
It is helpfull to get a machine that is meant to find the targets you are looking for and in this it should be jewelry I assume. So Gold Bug Pro is my first choice.
Another is the Garrett AT PRO....which is waterproof should you take a tumble. This can be had used for around similar price as the Fisher.
Below the $300.00 price range you lose some abilities to set the detector up that may or may not cause issues and hence ruin your fun. beach hunting is it's own animal and not like inland hunting. Cheap here can ruin a fun hobby.
Now if you are staying up in the dry coral sand...heck a Garrett Ace 350 or 250 may be just fine.
One thing to add....beaches are made up of different materials as we move around the globe. A detector may work fine in one area and not another. However seems like your island are either coral sand or volcanic sand....seems like those would be easy to detect on without getting false signals. Whereas i live in Maine and our beaches are all sand from granite..tons of black iron sand...and so can be a bugger for some detectors..even in the dry sand. Whereas when i went to South Carolina the beaches were coral and in the dry sand I could detect with anything....in the dry sand.
However there are other machines that would work too.....so what is your price range.
