It's great that you've decided to go vegan! I was vegan for about 6 months last year until I changed to a lacto-ovo diet due to low energy levels.
As far a eating cheaply goes, carrots, dried beans and cauliflower are your friends. The nutritional value of these three are awesome. Getting a large pot and some large tupperware and boiling the beans yourself/mixing them with veggies before a meal is a great time/money saver. You can then combine them with white or brown rice or any of the whole grains (my favorites are millet and buckwheat). You can make relatively cheap daily smoothies by mixing orange juice with frozen strawberries as well. You can buy a decently-sized blender pretty cheap, for around $20-25.
You can pretty easily make your diet more robust by adding whatever fruits you like at the moment. Some of them also help out with promoting active bowel movements (Especially Apples). Apples, Bananas, and Kiwis are my top picks. I'd also advise doing a cheap parasite cleanse (Black Walnut, Wormwood, & Cloves Tincture; Diatomaceous Earth; and Thyme/Oil of Oregano), followed by a good probiotic regimen. This will take ~2months to do, but you'll feel a lot better for it.
I agree about the need to take some ground flax seed/flax oil. I would cut back on oils in general and go more for avocados (a good Omega 3 source) if possible. Also, almond milk is a delicious substitute for cow's milk. Nuts in general are going to be your friends while on a vegan diet.
Have you considered going gluten free? That might be an excellent option to choose, although it might make eating within your diet a bit more difficult.
Lastly, I would try to eat raw as much as possible. If you keep at a vegan diet and don't go too hard on the sweets, all of your food will eventually start to taste better and sweeter; the diet takes some getting used to.