The brain does indeed run on glucose- that doesn't meant you need to eat sugar (or any high carb manufactured food). The body synthesises what it needs from protein and fat even if you ate 0% carb (which I'm not suggesting!!).
Protein is expensive, but many very good sources of protein and nutrients are not too expensive - eggs, cheese (if you eat dairy), liver and other organ meats, frozen newzealand lamb etc.
A whole chicken, even a free range organic one at around £12 roasted and then jointed up for breakfast/lunch meat to eat cold will cost less per portion than buying cold meats from the supermarket (which almost alway have a long list of additives and sugar in them).
Nuts are good too if you have no allergy issues with them.
Jane, I'm assuming by "good fats" you mean the fats that occur naturally on and in animal products, nuts and avocado, and not heat/chemically processed, structurally altered seed "veg" oils...
Associations between animal products and disease are exactly that - association. Which is not causation. On closer examination these studies rarely say anything like what the headline writers suggest and the association is tied in with consumption of processed meat products, high processed carbohydrate consumption and the use of growth hormones in farming. The studies are often looking at American diet, the growth hormones that are widespread there are banned across the whole of Europe. It's complex.
People eating, for example, a veggie diet might be healthier not because they are eating fewer animal products, but because being veggie is a marker for other life style changes (ie eat lots of unprocessed leaves bad veg, exercise more, avoid processed foods full of synthetic additives).
The book "death by food pyramid" by Denise Minger is a very interesting read about this whole subject - and about the manipulation of us, the consumer, for political (rather than health) reasons.
To sum up "Eat Real Food".
Unfortunately about 80% of the stuff in our supermarkets isn't real food, it's processed, extruded food-like carbohydrate things (cereals, crisps, biscuits take up most of the shelf space). Mutters ....it's The Wheat Industrial Complex...
Steps down from soap box and runs away 