The Internet of Things (IoT) is a growing area of technology and has been identified as a key tool for enhancing industries' operation and performance. As IoT deployment rises worldwide, so do the threats; hence, security, especially authentication and integrity, is a critical consideration. One significant future threat is quantum attacks, which can only be defeated using Post-Quantum (PQ) cryptosystems. New Digital Signature (DS) standards for PQ security have been selected by the US National Institute of Standards and Technology (NIST). However, IoT comes with its own technical challenges from the constrained resources allocated to sensors and other similar devices. As a consequence, the use and suitability of these PQ schemes for IoT remains an open research area. In this paper, we identify an IoT architecture built from three distinct layers represented by a server, a gateway and an IoT device, respectively. We first test PQ DS scheme standards and compare them with current standards in order to assess their practicality for use in this architecture to provide authentication and integrity. Then, we select the most suitable PQ scheme at each layer according to the features of the corresponding device (server, gateway, IoT device) and the security property (authentication, integrity). We finally carry out experiments on our selection and provide an architectural model for making IoT communication and interaction PQ secure.