Protein minus carbs, please!

Black pudding's a decent option - not zero carb, but not too high and pretty damn low fat as well. Cheap, too.

Don't know about where you are, but for me mussels don't cost a lot, and they're pretty much protein and nothing else. Be a bit careful, though - lots of purines, and if you're losing weight fast at the same time (ie metabolising a lot of body fat) you could be running the risk of giving yourself gout. I did. Not fun. Make sure you stay hydrated.

I'm not really sure what you're looking for here, but I'll just say how I do it--I eat low carb but don't restrict healthy fats, so most of my protein has fat along with it, or if it doesn't, I usually add some sort of healthy fat. I eat lots whole eggs, tuna, grass fed beef, grass fed pork, venison, duck, wild salmon, sausage, bacon, ...chicken is pretty low on my list of stuff I like/eat often.

I think the cheapest proteins I eat are probably whole eggs and canned tuna. I don't regularly eat dairy products, but if you do, that could be another option for you. Greek yogurt, cottage cheese, cheese, etc.

Carbs are everywhere--I mostly get mine through non-starchy veggies. I eat lots of spinach, kale, cauliflower, broccoli, peppers, tomatoes, asparagus, onions, and some squash and/or sweet potato here and there. If you eat fruit, you may find they add up quickly there, same goes for stuff like yogurt...any sort of processed foods also seem to ingredients that add to the carb total. Often times, "low fat" or "lite" or "reduced fat" products will be higher in carbs than the full fat versions. If you eat any sort of grains--rice, couscous, cereals, oatmeal, pastas, etc. check those for carbs, too. Sugars, stuff made from white potatoes, etc.

Shrimp!