Reading your other thread made me think of a recent post on I think Jeff Novick's face book page, which is all about plant centrix whole food diet and someone saying what they could do and they shopped at Walmart, so the budget link came in.
Nothing wrong with frozen vegetables and frozen potatoes and pre cooked beans if that gets you started on changing how you eat. There is also tinned fish or frozen fish, like everything that comes in a packet you need to look for there being no additivies, no sugar and no salt no preservatives and just being the plain food.
Your little one is young enough to grow with your food changes maybe little by little so they adapt. Perhaps others with toddlers can comment on how they changed their children too.
Don't go hungry this can be such a demotivator, have things you can eat like fresh fruit, dried fruit, cold baked potatoes, sold sweet potatoes, left overs from last night.
The first foods to remove would be meat and dairy, so what to replace with, meat would just be your whole food diet with pulses (beans) and some also do fish. Dairy is easy missed, if you have breakfast cereal then you could find a rice drink alternative some like soya but I personanly don't. Breakfast look for a plain muslie or even just plain porridge oats as this can be seetened with a little honey or chopped fruit and is the easiest to eat if warmed first in a pan with even just water and a good bowl is very filling. I am gluten free but do eat some oats but I totally avoid wheat.