I can definitely see flaws with some of your ideas. This all assumes these are normal Hollywood zombies. (zombie classique) Suppose they are zombies like in the movie 28 days later. (Which joking aside, is actually not that implausible). Those zombies are easy enough to kill but one drop of their blood on you and you join the horde! So in any melee situation you would be in great danger.
Therefore we would need stand off weapons of some sort. Shotguns, knives and any close in stuff would splatter you with brains and gore. Not nice.

So it has to be rifles and handguns and I think one that hasn't been mentioned here yet, mortars. You can zero in on concentration points in your defence perimeter with your mortar and zap them all. The island idea is nice but you would need forays to the mainland for supplies. Very risky.
Here in Ireland, which is in fact a big island, a better option would be to re-fortify an old castle or fortified house. The countryside is littered with them. Ironically many were built by the English to keep out marauding Irish. This is the one owned by Jeremy Irons the actor who is clearly ready for the impending Zombypocalyspe

Admittedly that's not really an option for Americans.

But, just re-fill the moat and get the boiling oil ready.
It worked in the middle ages and it will work now. We also have lots of round towers which were originally built to hold off the Vikings, surely the dark ages equivalent of zombies.

Once the zombie alert goes off, we all head into the tower, pull up the rope ladder and set about sniping at the zombies gathered below.