Arnel's diet, near as I can tell, is basically the same as phase 1 of the South Beach diet, but heavy on the protein. You don't have to eat egg whites at all, although eggs are one of the heapest things you can buy. But if you are low on money, here's some things that are good for you that you might want to try....
Dried beans... Soak them overnight then simmer them for a full day. They're high in protein and "good" carbohydrates.
Cheap Chicken... Buy the cheapest kind you can find, then spend the time with a knife to cut off all the fat, and either cut out the bone or just don't eat it. This is often the wings and thighs and drumsticks. If you have more money, buy the breast as it is easier to remove the fat and bones.
Vegetables... Buy as big bag of frozen mixed vegetables. Store brand, bigger bags are cheaper.
Eggs...you can eat 2 whole eggs a day without it being bad for your health, but if you want more protein you should just add more egg whites. Buy those 18 or 24 packs of eggs. They really aren't that expensive. Don't buy the organic unless you have the money to spare. Egg beaters (which are jsut the yolks) are way more expensive than buying the same number of eggs, in case you were considering that.
Peanuts...are a good food to eat. If you limit yourself to a serving at a time, a bottle can last a couple weeks. Buy the store brand "dry roasted" kind.
pork....this might be as cheap as chicken, just buy it with the bone and fat and cut it out yourself. Some kind of pork chops is probably the way to go.
Beef...I believe sirloin is the leanest beef for the price. Maybe the lean hamburger.
Tuna...Buy the store brand, in the biggest cans. One big can and a lot of vegetables makes a good meal. Maybe add in a little miracle whip (and salt and pepper) if you want to make it fancy.
Cereal...Buy something with lots of fiber, like "Fiber One" or the Kashi brand, or Kellog's All Bran. My personal favorites is probably Kellog's All Bran Strawberry Medley. Having some of that with the Hood low fat low carb milk works great.
Bread...Avoid anything that says "whole wheat." This is a a marketing gimmick. You really want the stuff that says "whole grain". The whole wheat stuff isn't much better than just eating some sugar. The whole grain stuff will give you energy without making you hungry. The downside is that it very grainy and dense and takes some getting used too. Near as I can tell, most whole grain bread is more expensive. I don't know why that is, since they are processing the grain less, but that's life, I guess.
Cottage cheese...whatever kind you like. IF you can stand it, buy the fat-free. I always buy the whole fat stuff, since it really isn't that high in fat anyway and has quite a bit of protein and is relatively low in carbs.
Anyway, I hope that helps a bit.