If you like square foot gardening, it sounds like a raised bed would be the easiest way for you to be successful. And if you are willing to do some labor, just do the following: Dig out your 4X4 bed 1 foot down, then add equal parts compost to that soil you dug out. Add that all back to bed and it should have a raised bed effect going. Then dig a trench around the border of the 4X4 bed at least 6" down and 4-5" wide. Add mulch to fill trench, then add more mulch to height of your raised bed. Voila!
This will now become your no-till bed. Don't put weight on it or walk on the bed. Continue to feed the bed with plants growing, it doesn't matter what you grow really, but one plant will not keep the bed happy. If you can care for one plant you can care for ten right next to it. With that said you are smart to start small.
Just start with your favorite vegetables as long as it makes sense where you live. I should put emphasis on growing something that suits your area; look for local seeds too that will help. Good luck!