I eat a pretty much vegan diet, I say "pretty much" because I still make regular cakes, etc for business and so it wouldn't be pc to say I'm a total vegan(there's that and the leather seats in my SUV!) Anyway, you don't have to go broke buying egg replacers. Ener G egg replacer is about $5 and will last you forever since 1 1/2 tsp = 1 egg and recipes that call for more than 4 eggs don't do too well with Ener G egg replacer so it will last you. For certain breads and brownies you can use a mashed banana. Tofu works well in cooked recipes (ex. puddings, custards) but you need to use the correct type of tofu for the job. Silked soft for puddings, silked firm for frosting. Play around with it to find the type you like best. 1 Tbsp vinegar = 1 egg in cake recipes but you'll have to test this to see which of your recipes works best with this technique. Also, club soda will make your cakes rise a bit more. Skip eggs in cookies, don't really need it. The following items have never worked well for me....soy powder, xantham gum, agar. Good luck and have fun and don't forget cakes will be more dense, heavy and cook a bit longer.
ps. If you can't have dairy/eggs because of health problems be careful and read your food labels. They get animals ingredients in just about everything nowadays.