High-quality panoramic images with a Field of View (FoV) of 360° are essential for contemporary panoramic computer vision tasks. However, conventional imaging systems come with sophisticated lens designs and heavy optical components. This disqualifies their usage in many mobile and wearable applications where thin and portable, minimalist imaging systems are desired. In this paper, we propose a Panoramic Computational Imaging Engine (PCIE) to achieve minimalist and high-quality panoramic imaging. With less than three spherical lenses, a Minimalist Panoramic Imaging Prototype (MPIP) is constructed based on the design of the Panoramic Annular Lens (PAL), but with low-quality imaging results due to aberrations and small image plane size. We propose two pipelines, i.e. Aberration Correction (AC) and Super-Resolution and Aberration Correction (SR&AC), to solve the image quality problems of MPIP, with imaging sensors of small and large pixel size, respectively. To leverage the prior information of the optical system, we propose a Point Spread Function (PSF) representation method to produce a PSF map as an additional modality. A PSF-aware Aberration-image Recovery Transformer (PART) is designed as a universal network for the two pipelines, in which the self-attention calculation and feature extraction are guided by the PSF map. We train PART on synthetic image pairs from simulation and put forward the PALHQ dataset to fill the gap of real-world high-quality PAL images for low-level vision. A comprehensive variety of experiments on synthetic and real-world benchmarks demonstrates the impressive imaging results of PCIE and the effectiveness of the PSF representation. We further deliver heuristic experimental findings for minimalist and high-quality panoramic imaging, in terms of the choices of prototype and pipeline, network architecture, training strategies, and dataset construction. Our dataset and code will be available at https://github.com/zju-jiangqi/PCIE-PART.