Ethnic markets usually have great prices. I did a blog post a few years back listing what I got for $57 at Lam's (in Phoenix). Prices have gone up a tad on some items (like everywhere else) but you can still find good bargains at most ethnic markets.http://karicooks.blogspot.com/2009/08/w ... ms-in.html
We also shop at Lee Lee's and at Sprouts (though I haven't been to Sprouts in a while).
Another store we checked out recently that has decent prices is WinCo. It's new to our area. If you're in a western state, there may be one near you. http://www.wincofoods.com/about/locations/
They have nice produce and a bulk section. Sometimes I get items at Sam's Club too. Recently they had some nice Brussels sprouts. Mmmmm. I think that's one of the few places I've seen fresh English peas sold.
I know that in Michigan, my mom does lots of her shopping at Aldi because their prices are so much cheaper. I've never been in an Aldi, though.
It would be hard to build a budget menu or shopping list for you. You'd have to go by what you like to eat and the costs of food in your specific area. Food prices can vary a lot by region. What's fairly cheap in one region might be crazy expensive (or not even available) in another.
If you have any ethnic markets near you, check them out.