Thought I'd answer from a bit of personal experience (I'm new on the board myself and haven't read all the archives.) I've got about 10 years eperience living on my own, and I've just recently gone paleo (about 5 months ago). I found out quickly that paleo is actually a less expensive way of eating - processed foods cost more in the long run. My advice is to make sure you eat what you buy. It's very easy to buy too much produce and then let it go to waste. Take the time to plan your meals for the week, and then shop to the plan. After a while you'll get a hang of it and won't have to spend so much time planning. I can now run through my farmers market and get everything I'll need for the week and risk little or nothing to waste.
The other option, if you're close enough to a fresh food source, is not to buy too much in advance. When I started, I would swing by the grocery store every morning to buy the produce I was going to eat that day. It gave me an appreciation for making good food choices. Not the best strategy for saving money right away, but it helps you learn some good lessons.