So great to see folks embracing self-sufficiency! As for vegetables, you can't go wrong with zucchini and tomatoes – they're productive and not too finicky. Vertical gardening techniques (like using trellises) can help maximize your space, which is especially helpful if you're lacking in that department.
Now, onto chickens: They're less maintenance than you might think! You'll need to provide them with a secure coop for nighttime and check on them at least once a day. They'll spend their days foraging for bugs, and in return, you get fresh eggs every day.
As for rainwater collection, it's great for watering your garden, but do check local laws first. Some areas have restrictions on this sort of thing.
Now, one thing you didn't mention but should absolutely consider is composting. It's a wonderful way to reduce waste and improve your soil quality. Have you given thought to starting a compost pile