The Armchair Economist is clearly written and interesting, but to me it's real value is in understanding how "supply-side" economists think. Much of the value is in trying to spot the hidden assumption or the logical fallacy.
As an example of the first: he argues that we should decide whether to do anything on global warming based on the monetary value people place on driving cars versus the monetary value other people place on not having their islands flooded. Ok, that's probably a self-consistent way of evaluating a policy, but there are at least two other frameworks for evaluation in common use that he doesn't mention: i) some idea of democracy, whereby the wishes of the (poorer) islanders have the same weight per person as the (richer) car drivers; ii) the idea of an external moral or ethical standard requiring that we avoid or minimise damage to the planet, independent of the opinions of others. Failure to acknowledge standards for decision making other than monetary seems a major flaw in the book.
The second weakness, the logical fallacy, is mainly illustrated whenever he demonstrates that two choices for economic policy have equal cost - e.g. a country paying for a something now versus borrowing money to pay for it; or making cars in the USA versus growing corn for export and buying cars from Japan. To a first approximation, he's correct in saying that the two alternatives are of equal cost. However at this point he should go on to consider the cost of second-order effects - e.g. the rising interest rate as borrowing increases, or the loss of future choice if the industrial capability to build cars is lost.
Since most or all of the book suffers from one or both of these problems, I wouldn't recommend this as a way of understanding economics, so much as a way of understanding economists. Given the importance of supply-side economists sharing his views, the book is useful to understand how and why economic policy is set.