The photogrammetric acquisition of 3D object models can be achieved by Structure from Motion (SfM) computation of photographs taken from multiple viewpoints. All-around 3D models of small artefacts with complex geometry can be difficult to acquire photogrammetrically and the precision of the acquired models can be diminished by the generic application of automated photogrammetric workflows. In this paper, we present two versions of a complete rotary photogrammetric system and an automated workflow for all-around, precise, reliable and low-cost acquisitions of large numbers of small artefacts, together with consideration of the visual quality of the model textures. The acquisition systems comprise a turntable and (i) a computer and digital camera or (ii) a smartphone designed to be ultra-low cost (less than $150). Experimental results are presented which demonstrate an acquisition precision of less than 40 µm using a 12.2 Megapixel digital camera and less than 80 µm using an 8 Megapixel smartphone. The novel contribution of this work centres on the design of an automated solution that achieves high-precision, photographically textured 3D acquisitions at a fraction of the cost of currently available systems. This could significantly benefit the digitisation efforts of collectors, curators and archaeologists as well as the wider population.