We've got 3 garden plots and a few raised beds. All are fenced and in our backyard which is also fenced and holds very large, cranky dogs. I've had problems in the past with a woman that used to live up the road, she seemed to think that my garden and chicken house was a public food distribution point. Caught her leaving my chicken house one day carrying a dozen eggs, and she couldn't understand why I was angry. We extended our yard fencing to encompass the chickens and gardens and she didn't come back because she didn't like the dogs that would stop her. She had the gall to complain at the little general store about me, said I wasn't neighborly since she couldn't go get what she wanted whenever she wanted to, the people there told her that she was lucky to not have a backside filled with rock salt.
As to easy vegetables to grow. Try summer squash, I think that stuff would make it through a nuclear holocaust.