In this work, we consider Terahertz (THz) communications with low-resolution uniform quantization and spatial oversampling at the receiver side, corresponding to a single-input multiple-output (SIMO) transmission. We fairly compare different analog-to-digital converter (ADC) parametrizations by keeping the ADC power consumption constant. Here, 1-, 2-, and 3-bit quantization is investigated with different oversampling factors. We analytically compute the statistics of the detection variable, and we propose the optimal and several suboptimal detection schemes for arbitrary quantization resolutions. Then, we evaluate the symbol error rate (SER) of the different detectors for 16- and 64-ary quadrature amplitude modulation (QAM). The results indicate that there is a noticeable performance degradation of the suboptimal detectors compared to the optimal detector when the constellation size is larger than the number of quantization levels. Furthermore, at low signal-to-noise ratios (SNRs), 1-bit quantization outperforms 2- and 3-bit quantization, respectively, even when employing higher-order constellations. We confirm our analytical results by Monte Carlo simulations. Both a pure line-of-sight (LoS) and a more realistically modeled indoor THz channel are considered. Then, we optimize the input signal constellation with respect to SER for 1- and 2-bit quantization. The results give insights for optimizing higher-order constellations for arbitrary quantization resolutions and show that the minimum SER can be lowered significantly by appropriately placing the constellation points.