Low cost meals that are low in carbs?

I like to make spaghetti for the kids, then mix my marinara with some cheap ground beef. I'll serve them pasta, and have mine with veggies. I like squash(cheap this time of year), zucchini (just sliced and steamed). But you could do any veggies you like.

I think breakfast and lunch could be done on the cheap. Dinner, honestly, is harder. (Case in point, my kids are eating pizza. I’m eating chicken tonight. My husband ate a salad). Maybe do lower carb breakfast (I love eggs and bacon) and lunch and just eat a smaller portion of a slightly higher carb dinner,

I guess it depends on what you like. I eat kale most days. It's only $1 per bunch, which usually lasts me the whole week. I cook it in water til soft, season with soy sauce, then add an egg or two and a small drizzle of sesame oil.
Ground turkey is cheaper than ground beef, you can serve it with spaghetti sauce and zoodles or pasta or do a turkey taco salad(taco seasoning, chopped lettuce and tomatoes). Meat patties with mushrooms and side veggies.
Also, just look for sales on meat. Pair whatever protein you like or is on sale with vegetables you and your family like. You and the kids don't necessarily have to eat all the same veggies. My nephews love raw veggies with ranch or hummus, as well as many fruits. So I just offer them a few choices of fruit/veg with their meat/protein (sometimes it's cheese, beans, or tofu).

Hmm...”safe” and “fast” are opposite ways of losing weight , unless you’re doing medically supervised weight loss. In that case, your doctor should guide you on what and how much to eat.