As far as low cost goes, eggs, ground meats, and frozen vegetables are some of the least expensive items that are great on a low carb diet. I buy in bulk, and freeze in smaller amounts. I only do this when even bulk items are on sale. I also have found that our local grocery stores have the most items marked down for quick sale on Tuesday mornings. I go shopping around 9:00 am, and can find fresh prepackaged salad bags and bowls that are normally $3.99 for 99 cents each. I can also find ground meats, steaks, chops and boneless skinless chicken breast and thighs marked down a great deal on those days. They are either at the sell by date or 1 day before the sell by date. Use or freeze that day and they are still perfectly fresh. I have a vaccuum sealer, so that helps buying in bulk. But even if you buy very inexpensive freezer bags and use 2 (put meat in bag, push out as much air as possible and seal, then place sealed side down in 2nd bag, push out air, and seal again) you still save money over buying 1 pound portions. Also, use coupons if you have them for canned and frozen vegetables, and on the rare occasion when they have them, meats. If you have an opportunity to do so, try shopping on different days of the week to see if you find this is the case at your grocery store as well.
I am living life "On the Beach" so many of my recipes have more than 10 carbs. However, I have printed out a cookbook for myself, putting them in a binder in clear sheets. The numbers in paranthesis are TOTAL CARBS, NOT NET CARBS! There are 2 links to another website, Linda's Low Carb. Some of her recipes are inexpensive, other more expensive. You might want to check out some of her other recipes from the 2 I linked. I will list some of the recipes I believe fit your requirements!
Appetizers:
Chicken on a Stick (3.9)
Teriyaki Beef Skewers (4.3)
Breakfast:
South Beach Diet Bacon Egg Muffins (1.3)
Sausage and Cheese Breakfast Cups-South Beach Diet (3.6)
Breakfast Mock Cinnabon (low Carb) (5.1)
Meat:
Beef:
Peppers and Steak for the Crock Pot (4.5)
Dijon Burgers (2.
Mushroom Burgers (1.7)
Chicken:
Parmesan Fried Chicken (2.7)
Chicken Capri (3.1)
Cheesy Bacon and Garlic Chicken (1.
Turn Your Crockpot Into a Smokehouse Chicken (0.0...depending on the liquid smoke brand, make sure it is water and smoke only)
Low Carb Sausage, Mushroom, and Chicken Casserole (5.1...I use canned mushrooms. Great for leftover chicken in recipe above)
Pork:
boneless pork chops (0.3)
Easy Pork Chops (3.0)
Vegetables:
Broccoli Salad (4.0...I sometimes add splenda to this, which ups the carb count a little)
http://www.genaw.com/lowcarb/broccoli_mushroom_casserole.html (5-8 carbs, depending on serving size)
http://www.genaw.com/lowcarb/dotties_green_bean_casserole.html (5-7 carbs, depending on serving size)
Soup/Chili:
"All-You-Can-Eat Soup Diet" Soup (7.6...I like this, but I have to add LOTS of seasoning to it, such as paprika, oregano, and extra salt, pepper, and chicken bouillon. Sometimes I start it with part chicken broth and part water...seems to have better flavor. I use frozen cauliflower, squash etc. when out of season and fresh costs too much.
Low Carb Chili (8.6)
Desserts:
Sugarless Flourless Peanut Butter Cookies (2.1, not including splenda. I always omit the baking soda. )
Cheesecake--Low Carb (3.2, not including splenda)