Horse manure or an organic mix such as Rose Tone, Mill's Magic Rose Mix or a similar home made concoction.
The above feeds, enriches, and loosens the soil. It also aids in drainage in clay and water retention in sand. It provides food for worms and soil organisms that aerate the soil. It's important that oxygen gets to the roots.
Chemical fertilizers are like candy and junk food. They provide fast acting nutrients but don't last long in the soil.

There are really different philosophies out there about the best way to fertilize your garden, no matter what you are growing. karl_bapst_rosenut's advice is classic organic gardening advice with regards to fertilization. If you choose to follow an organic (or mostly organic) gardening style then the most important thing you can do is learn about your soil. In gardening generally, but in organic gardening in particular, the best way to feed your plants is to feed your soil so the soil is functioning in a healthy manner.

I don't know where exactly on Long Island you live (& don't really want to know), but unless it's in Queens, Brooklyn, or one of the suburbs close to there (or along the northern shore in one of the higher elevations, such as Oyster Bay, or some such) the chances are your soil has a decent amount of sand in it (the further out on LI you live the greater the percentage of sand your garden's soil is likely to have). Sand creates a very particular soil environment that is in some ways useful, and in other ways challenging.

What's nice about using an organic style to fertilizing your garden is that the challenges presented by sand (or silt, or clay) are often best met by the soil fertilizing techniques used by organic gardeners.

--Chemical fertilizers are like candy and junk food. They provide fast acting nutrients but don't last long in the soil.--

That's not exactly true, but I know what you are trying to say. Nutrients are nutrients. Nitrogen is nitrogen and phosphorous is phosphorous and potassium is potassium. It doesn't matter one bit to the plant whether it comes from an organic source such as blood/bone meal, grains, etc.. or from a synthetic fertilizer. It is all the same to the plant. The difference is what these fertilizers do to the soil. Organics feed the soil and improve soil structure. Synthetics do not. After years and years of using organics, you soil will be enriched, there will be more organic matter that will hold moisture, while still being well draining, and will have improved/excellent soil structure. After years of feeding synthetics, your soil will be the same as when you started. The soil structure will not have been improved. There will be no more organic material than before, it will drain the same, etc.... Synthetic ferts will improve your soil over time, snythetics will not. That is where the benefit of organic fertilizers comes into play, not so much the nutrients they provide to the plants.