Find your county extension office and talk to a Master Gardener. Those folks love to teach newbies

. it's free, and they have tons of resources about your specific area you won't be able to necessarily find on line. They can take you from ground zero to preserved in jars, I kid you not. Wonderful, under-utilized resource.
This is exactly what I’d suggest. All gardening is local. We each have our own microclimates, our own soil types, and our own methods. Some plant in rows in the ground which many people consider the traditional farmer’s garden but you also have containers, raised beds, square foot, and other methods. I don’t know which would be best for you.
Your local master gardeners will know what grows in your area and will know what varieties of things grow best in your area. They can tell you where to get seeds and started plants, mulch or compost. They can help you start your own compost pile which I strongly suggest you do. I’m also a big believer in the power of mulching.
The extension office should have all kinds of free brochures that tell you how to grow things. One of the more helpful things I got was a calendar that tells you what you can plant every month. That not only tells you when to plant something, it tells you what grows in your area.
I agree you need a good fence. With neighbors like that you might need a good padlock on the gate.
If you want you can join us on the sister gardening site. It’s a fairly small group that is really friendly and welcoming. We tease each other and have fun but there are some serious gardeners on there when it comes to gardening. Right now we are not talking that much about gardening since it is kind of off season, but if you have questions you can get some answers and see photos.
http://www.theeasygarden.com/
My other suggestion is to start small. Gardening is a time commitment. It takes time to prepare the ground, plant things, keep weeds and grass out, prune and maintain, and even harvest and preserve. A lot of people start out really big and burn out. Plant just a few easy things the first year to learn the techniques, how much you need to plant for your family, and to have some successes. This is probably the hardest thing to do. It’s hard to look at seed catalogs or visit gardening centers and not get carried away.