I have been vegan for 4 years now and like any other nutrition you can spend a lot of money on it, but also focus on cheaper products instead. And meat and cheese can be also very expensive, so that by leaving them out, you will substantially cut your costs.
For breakfast for example porridge with soy-rice milk and some fruits, for lunch some fruits or bread with hummus and for dinner vegetables with rice or potatoes and a tomato sauce. Depending on where you live, certain fruits and veggies are less pricy - most of the time the seasonal and local produce is the best choice here. Some supermarkets also offer second choice foods that most of the time are perfectly fine, with just a few visual flaws.
If you and your roommate want to make sure that you get all the nutrients you need, easily track your intake with the app Cronometer. This way you can ensure, that you are on the best path to a healthier and stronger body ;)