Gamma-ray bursts (GRBs), particularly those detected by wide-field instruments such as the Fermi/GBM, pose challenges for optical follow-up because of their large initial localization regions, leaving many GRBs without identified afterglows. The Gravitational-wave Optical Transient Observer (GOTO), with its wide field of view, dual-site coverage, and robotic rapid-response capability, bridges this gap by rapidly identifying and localizing afterglows from alerts issued by space-based facilities including Fermi, SVOM, Swift, and the EP, providing early optical positions for coordinated multiwavelength follow-up. In this paper, we present optical afterglow localization and multiband follow-up of five Fermi/GBM (240619A, 240910A, 240916A, 241002B, and 241228B) and two MAXI/GSC (240122A and 240225B) triggered long GRBs discovered by GOTO in 2024. Spectroscopy for six GRBs (no spectroscopy for GRB 241002B) with VLT/X-shooter and GTC/OSIRIS yields precise redshifts spanning $z\approx 0.40$─3.16 and absorption-line diagnostics of hosts and intervening systems. Radio detections for four events (240122A, 240619A, 240910A, and 240916A) confirm the presence of long-lived synchrotron emission. Prompt-emission analysis with Fermi and MAXI data reveals a spectrally hard population, with two bursts lying $>3\sigma$ above the Amati relation. Although their optical afterglows resemble those of typical long GRBs, the prompt spectra are consistently harder than the long-GRB average. Broad-band afterglow modelling of six GOTO-discovered GRBs yields jet half-opening angles of a few degrees and beaming-corrected kinetic energies $E_{\rm jet}\sim 10^{51}$─$10^{52}$ erg, consistent with the canonical long-GRB population. These findings suggest that optical discovery of poorly localized GRBs is likely subject to observational biases favouring luminous events with high spectral peak energy ($E_{\rm p}$), while also providing insight into jet microphysics and central engine diversity.