Because you are so near to the shoreline, you face many challenges in growing plants that your inland neighbors will not have to deal with. Plants at a seaside location will be affected by the sea spray and must be able to tolerate a certain amount of saline environment. Also, you will be faced with challenges from the heat, porous sandy soil and the ever-present winds. My first suggestion would be to contact the Galveston County Extension Office and request copies of these two pamphlets: B-5015, "Landscape Development for Texas Coastal Areas" and GC-108, "Plants for Texas Coastal Areas". Both pamphlets contain a wealth of information about plants that can be successfully grown in seaside communities. Also, you should use local, native plants as much as possible and analyze what is healthy and growing in neighboring yards, and ask around; most gardeners are always willing to share their ideas and experience.
For your consideration in planning your landscape, some planting suggestions follow. Groundcovers such as asparagus ferns, Virginia creeper, Asiatic jasmine, confederate jasmine, native trailing lantana and wedelia should be able to withstand some of the seaside conditions. Two vines recommended for your area are cape honeysuckle and the Virginia creeper. Trees that can tolerate coastal conditions are the chinaberry, Aleppo pine, goat willow, mimosa, and the tamarisk. Small shrubs that should do well are the century plant, pampas grass, prickly pear cactus, rosemary and yucca. In the medium shrub range, you will be able to choose from elaeagnus, yaupon, wax myrtle, hibiscus and pittosporum. Oleanders, both dwarf and large, do well in the coastal areas and come in a wide range of colored flowers. Grasses recommended for the beach area are sea coast blue stem, salt grass, sand knot grass and giant sea oats. Several palms that do well are the palmetto palm, the Texas palmetto, cabbage or Florida palm and the Washington fan palm. For spots of color, consider perennials such as gaillardia (the native Texas Indian blanket) and purslane. The above are only a few plants to consider; the two pamphlets identified earlier offer much wider listings.
If you are directly on the Gulf, you may need to construct some sort of protection to deflect the wind, blowing sands and salt spray. This could be in the form of windbreaks either natural or manmade. Fences, walls, berms, hedges or natural sand dunes all help to absorb some of the brunt of the wind and sea and thus give you plants a better chance for survival.
Since land so near the water's edge is mostly sand, you should add lots of organic matter such as peat, compost or shredded bark mulch to improve the soil's ability to retain moisture. If your yard has recently been under water due to a tropical storm, you may need to replace the existing topsoil to decrease the salt content in your landscaping location. It takes several good rains to leach the salt from soil that has been flooded.
Over time, salt spray will accumulate on your plants' leaves and you should routinely hose them down. Watering deeply will also leach the salt in the soil to a depth where it will be less harmful to your plants.