Answer: Wonderful! Yes, all of the crops you mention do well in your area. First, choose the sunniest part of your property for the garden. Vegetables will produce best in full sun, but will produce some yields if you get at least 6 hours of sun. Good drainage is also essential.
Next, dig up the sod and shake as much soil from it as you can. It's easier to do this if you moisten the area first (especially since it's been so dry lately) and let it sit overnight. If you have access to compost, spread it 1" thick over the area and mix it in. Correct soil acidity is crucial for good plant growth. You can purchase a home pH test (Burpee has one) to see where yours stands. For a full report of the health of your soil, have a soil test done, and amend the soil based on the resulting recommendations. The New York Agricultural extension service (ph# 212/566-0673) can help you with a soil test.
It's a little too late to start your tomatoes and peppers from seed, since they need a long growing season, so purchase plants. Tomatoes will be healthier and produce better if caged or staked. Onion seed takes even longer, but you can plant sets (tiny onion bulbs) that will supply you with scallions and storage onions. Plant seeds of lettuce and beans right into the garden. Directions for planting should be right on the seed packets.
Lay mulch between rows and between plants to keep weeds under control. A simple inexpensive mulch is newspaper covered with straw, grass clippings and/or shredded leaves. Moisten the soil well before planting, and keep soil evenly moist with frequent watering. Soaker hoses are an easy way to provide needed moisture to your garden, are easy to install, and save a lot of time and effort. Fertlize the garden with a balanced fertilizer (5-5-5 or 10-10-10) applied at the rate suggested on the label. Be careful not to overfertilize -- it can cause just as many problems as not adding enough.
I think that's enough to get you started -- our FAQ database has lots of tips to answer your specific questions, or feel free to ask more questions via the Q&A page. Best of luck to you!
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