Eggs are super cheap. Buy whatever veggies and fruits are on sale. If your budget is really that tight, it's not paleo, but rice is cheap and is generally well digested by most people. Very carb-y unfortunately, but better than eating processed food and not feeling well.
It's tempting to buy processed foods because they appear cheap (especially when they are on sale.) But honestly, since going primal, I find my grocery bills have mostly stayed the same and sometimes have even gone down.
Breakfast: I bought two dozen eggs ($3), a pound of ground pork from the counter ($2), an 8 ounce block of cheddar cheese (frequently on sale for $2.) $7 total. I made 24 breakfast muffins from all this, and I eat two for breakfast, so it makes 12 breakfasts.
That is 58 cents per breakfast.
Lunch is an apple and natural peanut butter - not paleo or primal, but I'm on a tight budget too, so I buy the PB instead of almond butter. The peanut butter is $2.79 for a jar if I haven't bought it on sale. 16 ounces, that's 32 tablespoons, 16 two tablespoon servings or 17 cents per serving. The average apple, rounding up, is about a quarter of a pound. Apples are about $2/pound if they're not on sale, so 50 cents for the apple.
67 cents.
Snack is two ounces of cheese sliced off an 8 ounce block, so 50 cents for the cheese, and a quarter cup of almonds, bought in bulk, 48 ounces for $12 - a quarter per ounce, quarter cup is two ounces so 50 cents.
Last night I ate pork meatballs and sweet potato for dinner. The pork was $2 for a pound and I ate half of it. The sweet potato was 79 cents a pound - it wasn't actually a full pound, but let's say it was. $1.79.
58 cents + 67 cents + $1 + $1.79 = $4.04. And all of that is rounded up on weights, and assumes I didn't buy anything but the cheese on sale (cheese is ALWAYS on sale here!)
Even if I were eating almond butter, that would still land me under $5/day to eat fully primal. About the only way I could think to beat that and make a significant cost difference would be if I were eating ramen for every meal.
All that lands me at 1800 calories, 104g of protein, 125g of fat, and 58g net carbs. Protein could be a bit higher but not too bad.
It really is tempting to buy the packaged stuff because that's the stuff that always has big flashy sale tags on it, and veggies and fruit often don't. I haven't seen apples on sale for almost a month here, any variety. During the winter at least one variety was on sale every week. But when you actually calculate it out, it's surprising how much money you aren't saving. Eating healthy doesn't have to be expensive! You don't have to buy almond flour or coconut flour, or big jars of coconut oil, organic produce, grass-fed meats, or whatever else "paleo people" will tell you to pick up. Buy the best meat you can - for me that means I buy stuff they pack up fresh at the meat counter rather than something pre-packaged and branded - pick good fruits and veggies. An apple is going to cost me about the same as a package of ramen but it's NOT going to make me feel like crap.
I wouldn't even be super concerned with weight loss right now... just worry about eating well. It will help you feel better overall.