The Future of Food is Litty McGee
This article roughly estimates a healthy cost per meal for your use in a budget, and mentions related services of interest.
Food is awesome. I'm fortunate enough to have a wife that can cook, some cooking skills of my own, a living location in proximity to many good restaurants, and a budget to more or less do as I please. Should I just eat the tastiest food? Nope. Health matters, and even though I could spend a ton on food it would be cool not to.
I don't even consider eating out a sustainable thing for the purpose of a budget, with the possible exception of Subway. When designing a budget we should keep separate line items for necessary and recreational eating. This article targets the necessary part. We begin by defining the cheap and expensive limits, then attempt to winnow down a more or less ideal price point, acknowledging that personal factors will cause this to vary somewhat.
The cheapest possible meal, or within a few cents anyway, is crappy Ramen and Lipton Tea. You could drink tap water but Lipton does a great job of masking the crappy taste and comes in at 2 cents per serving. I did at one time survive for a couple months on a disgusting diet of oatmeal for breakfast with Ramen for lunch and dinner. Oatmeal with raisins and occasionally a bit of sugar runs about the same as crappy Ramen (Maruchan or Nissin) in terms of price: Under $.20 per serving.
On the other end of the spectrum we have Blue Apron and it's competitors. I use Blue Apron and I recommend it. It's high quality, though arguably not the best-in-class. I like it because it is either cheapest-in-class or nearly so, where the whole class is high quality. Very healthy, plenty of variety, I could (and do) it the stuff for days on end.
The obvious concern with the cheap option is health. <a href="http://www.planetforward.org/2014/11/21/the-ramen-noodle-diet-not-just-for-college-students">This article highlights some of the issues. Perhaps the largest issue complained about in articles on the topic is the level of sodium, but in practice it's easy to use less sodium. I think the stuff is too salty anyway if you use the whole included packet. In the cup-style ones you can eat the noodles and dump the liquid. Still, sodium is not the only health concern. In short, this isn't a sustainable budget or diet. You can do it occasionally, but you would save even more money and relatively improve your health by simply fasting on occasion.
There are two other problems with food that I want to consider: edibility and time. Honestly, I can't stomach a 100% Ramen diet. I've tried it. It makes me gag. I can do like 1 meal a day, sometimes 2, with discomfort. I can do Blue Apron all day, but you have to cook the stuff which takes time and energy. Enter <a href="https://www.soylent.com/product/drink/">Soylent and soylent-like products (there are several competitors).
Soylent is one of the future things I will mention here. Blue Apron kind of is. The other two are <a href="https://www.movebutter.com/">Movebutter and <a href="https://www.reddit.com/r/Frugal/comments/6p1y90/what_do_you_guys_think_of_the_kickstarter_public/">Public Goods. Just check them out I'm not elaborating. Also, there's the whole Amazon bought Whole Foods thing which you know will eventually turn into some sort of reduced cost, high-quality grocery service.
Soylent comes as a powder meal replacement shake, or in a bottle where they've already mixed it for you. The powder is just over $1.50 per serving, but call it $1.75 for tax and shipping. The bottles come in a variety of flavors with the plain kind being $2.50 and the fancy kind being $3.20 ish. Soylent has a somewhat milky flavor and Some of the fancier ones are mixed with coffee so they include caffeine, another interesting consideration as it substitutes to some degree for coffee and may perk productivity.
In either case you save time relative to cooking, but you save the most time with the pre-mixed drink. It's also not lumpy if you get the bottles. The thing is, many folks have gone 30 days+ just eating this stuff. They've gotten blood work done and everything. It's nutritionally balanced in terms of macros and vitamins, it's really quite healthy. Here's <a href="https://www.producthunt.com/posts/soylent-2-0">one interesting review by a dude who is an athlete and an entrepreneur. He got blood work done as well. It's not perfect: It includes soy and a bit of sucralose and some other stuff, but I say it is more than tolerably healthy as a baseline in your budget.
Consider <a href="http://www.webmd.com/food-recipes/features/cheap-healthy-15-nutritious-foods-about-2-dollars#1">this article from WebMD which demonstrates plenty of healthy recipes you can cook for less than $2 per serving. Keep in mind that many of these are subject to lumpy pricing, which means you can't exactly buy the ingredients for a single serving. Instead you have to buy at least like 6 or a dozen or X number of servings at a time because of the nature of the recipes or the way the ingredients are sold (eg a loaf of bread, a pack of hot dogs).
So, the recommended numbers: $2 per serving which you plan on cooking. $4 per serving which you don't plan on cooking, but you do plan to buy as a grocery. These are minimums. In your actual budget you should be honest about how much you plan to spend. I eat Subway for lunch most days, so I budget like $9 per lunch. If I were in a tight money situation, though, or if I was somehow really motivated to save like $100/month, I could bring food from my house. I also recommend budgeting for spending money as a separate line item, and you can expense splurge meals against that amount.
Are you going off budget or want to save up a bit? It doesn't hurt to eat a lower quality meal or skip a meal or even fast a whole day on occasion. In fact, intermittent fasting may be quite good for you. Just be careful not to do this stuff too frequently or you may harm your health. Also, keep in mind that if you are already getting sick this might weaken your immune system, or give you a bit of a headache and reduce your ability to focus, or make you a bit tired.