My family is vegan (although one of my sons does eat meat when he goes out, just not at family meals). Not buying meat is very helpful for the budget! If you don't want to go completely meat-free, you could always trying having a day or two of meat-free meals which would save you some money.
Even before we were all vegan, I liked Thomas Jefferson's approach of planning meals around vegetables and treating the meat as "seasoning." When I was younger, I planned meals by first deciding which kind of meat we'd have - chicken, ground beef, pork chops - then adding the other parts of the meal.
When I became more concerned about healthy eating, I learned to plan my meals around the vegetables instead. We always have at least two vegetables with dinner - that's important for us in achieving my goal of nine servings of fruit and vegetables a day, and getting plenty of variety. So I start by seeing what fresh vegetables I have that I want to use up, and then what other vegetables (frozen, usually) can be added. Then I'll add some kind of whole-foods starch (a whole grain like brown rice or barley, or a whole-grain pasta, or unpeeled sweet or white potatoes, or corn) and finally think about protein. That might be a peanut sauce on the vegetables, or some beans, or hummus. Or I might not worry about it, since there's usually plenty of protein in the starch/vegetable combinations.
I think that planning this way has helped me keep the costs of my meals low but nutritious.
Teresa