Frost tolerant vegetables such as lettuce, spinach and other greens are known as cool season crops and they can be planted about 30 days before the last frost-free date for your area. These plants will withstand an occasional frost without being damaged. The other vegetable crops are more sensitive to frost and cool weather even if it doesn't frost. Often warm season plants will not grow at all when soil temperatures are below 60 degrees.
Lettuce (cool season)
There are 4 types of lettuce: leaf, butter head, crisp-head and romaine. Most are extremely easy to grow except the the crisp-head lettuce. Stick with leaf type lettuces for your first efforts. Lettuce leaves can be picked anytime up till the time it bolts (sends a taller stalk that flowers to produce seed)
Broccoli (cool season)
Broccoli grows best during cool season temperatures; when temperatures warm the broccoli heads will flower very quickly. Some varieties will send out side shoots once the main head has been harvested.
Tomatoes (warm season)
There are many varieties of tomatoes today so you could be overwhelmed with the selections. Look for varieties that are disease resistant. Tomatoes can be planted in a variety of ways from free-form, staked, caged, potted, even upside-down. When planting, remove the lower leaves and any flowers on the plant before planting. When transplanting from a seed tray or pot, set the plant as deep as possible in the soil without covering the top cluster of leaves. Don't bury leaves, but pick them off before planting. Some of the smaller (grape-type) may reseed and come back the following year depending on temperatures.
Peppers (warm season)
Peppers are an extremely easy plant to grow. Once in the ground, peppers need little additional care other than to make sure they get enough water, especially during hot, dry weather conditions.
Green Beans (warm season)
Best grown from seed and planted a weekly intervals to spread the harvest dates .