Single-pixel imaging is an imaging technique that has recently attracted a lot of attention from several areas. This paper presents a study on the influence of the Hadamard basis ordering on the image reconstruction quality, using simulation and experimental methods. During this work, five different orderings, Natural, Walsh, Cake-cutting, High Frequency and Random orders, along with two different reconstruction algorithms, TVAL3 and NESTA, were tested. Also, three different noise levels and compression ratios from 0.1 to 1 were evaluated. A single-pixel camera was developed using a digital micromirror device for the experimental phase. For a compression ratio of 0.1, the Cake-cutting order achieved the best reconstruction quality, while the best contrast was achieved by Walsh order. For compression ratios of 0.5, the Walsh and Cake-cutting orders achieved similar results. Both Walsh and Cake-cutting orders reconstructed the images with good quality using compression ratios from 0.3. Finally, the TVAL3 algorithm showed better image reconstruction quality, in comparison with NESTA, when considering compression ratios from 0.1 to 0.5.