Also I reckon I could write a book on bulking on a budget, here's the thing though, high protein calorie rich foods are all pretty cheap
Brown meat chicken IE thighs and drumsticks, rice, milk, budget/economy BBQ steaks, root veggies, canned tuna, oats etc arent budget bulking foods theyre just budget foods. Might be different in America but those are literally the cheapest foods here in Australia.
Get yourself a rice cooker and always have rice made, learn to slow cook budget cuts of meat which when cooked right kill all the premium cuts anyway, freeze your milk when its on special etc getting way off track but you should aim to do one shop per week for food, towards the end of the cycle you will be slumming it but youre not alone mate Im struggling over here too with two kids, two mortgages and a single income.