The open science movement has gained significant momentum within the last few years. This comes along with the need to store and share research artefacts, such as publications and research data. For this purpose, research repositories need to be established. A variety of solutions exist for implementing such repositories, covering diverse features, ranging from custom depositing workflows to social media-like functions. In this article, we introduce the FAIREST principles, a framework inspired by the well-known FAIR principles, but designed to provide a set of metrics for assessing and selecting solutions for creating digital repositories for research artefacts. The goal is to support decision makers in choosing such a solution when planning for a repository, especially at an institutional level. The metrics included are therefore based on two pillars: (1) an analysis of established features and functionalities, drawn from existing dedicated, general purpose and commonly used solutions, and (2) a literature review on general requirements for digital repositories for research artefacts and related systems. We further describe an assessment of 11 widespread solutions, with the goal to provide an overview of the current landscape of research data repository solutions, identifying gaps and research challenges to be addressed.