I think you can look at this from a standpoint of emphasis and presupposition. When you put the modifier after the noun, you make it clear that it's the modifier that's the new information; everything else is presupposed (assumed beforehand). You can also make that clear by using inflection to emphasize the adjective or by making the contrast explicit: "Buy second hand things [instead of new things]."
You can think of the statements as answering different questions. (The question might not literally be asked: it might be implied by the information required in the situation, which is why there are situations, like this one, in which either construction would work.)
How should I buy things in order to save money? [The question implies you're already planning to buy things.] Buy things secondhand.
What should I do in order to save money? [You're not aiming in any particular direction.] Buy second-hand things.
Or, to take a different example:
How does she take coffee? [The question implies we already know she likes coffee.] She likes coffee black.
What does she like to drink? [We have no idea if she likes coffee.] She likes black coffee.
The presuppositions in (1) and (3) are that you buy things and that she drinks coffee, and the answers being given address how (second-hand, not new; black, not sweetened). This works in the second-hand situation in the magazine article because the reader probably does buy things, so the presupposition is accurate. If the advice were "save money by buying telegraph equipment second-hand," it would seem odd because it would presuppose that the average reader regularly purchases telegraph equipment. Essentially, the message is "When do you buy things [which you already do], buy them secondhand," whereas "Buy secondhand things" connotes "Buy things [maybe you don't already?], and buy those things secondhand."
In this case, I would say that the adjective-second construction is slightly more suited to the situation because in the unlikely event that you don't currently buy things, taking up a habit of buying second-hand things won't save you money. The money-saving property comes specifically from the contrast with buying things new, and this construction highlights that contrast.