For the poverty part, there are no cheap options. You go to a chicken factory, for a hundred bucks you can get enough processed chicken to feed you for a month. I've been there, many times. So broke you need to make 25 a week spread. Buy the healthy shit and you eat for a couple days, tops.
But, and here is the kicker, you eat that shit for long enough, whether out of desperation or choice or whatever, that is what starts being normal. This is what food tastes like, because you have always had it. Then you eat the good quality stuff and it tastes bad, because it isn't the bad food you know.
And when you are that broke, you aren't going anywhere. A gym membership is half your food bill. You can't afford to do anything so you don't do anything.
I know being broke. I know eating bad, and the reasons for it. There is no way to eat healthy in true poverty. At all.