Donald Trump never skips a chance to remind audiences of his wealth, but he is proving reluctant to spend his own money on campaign essentials typical of a major presidential candidate.

The New York developer has rejected paid television advertising as unnecessary, and he has resisted investing in efforts to secure ballot access, which can be expensive in some states, according to people familiar with his campaign. He also is rejecting appeals from his staff to appear at more in-person events, the people said, building his...