Hi Stuart,
First, let's tackle the background information:
What is ArcGIS Online?—ArcGIS Online Help | ArcGIS
What is ArcGIS Enterprise?—ArcGIS Enterprise | ArcGIS Enterprise
ArcGIS Pro | ArcGIS Desktop
So, after reading through that, you should have a much better understanding of the 3 products.
The TL;DR,
ArcGIS Online is a SaaS offered by Esri. ArcGIS Online is a cloud-based mapping and analysis solution. Use it to make maps, analyze data, and to share and collaborate. Get access to workflow-specific apps, maps and data from around the globe, and tools for being mobile in the field. Your data and maps are stored in a secure and private infrastructure and can be configured to meet your mapping and IT requirements.
ArcGIS Enterprise is an on-premise or cloud based single tenant WebGIS. ArcGIS Enterprise puts collaboration and flexibility at the center of your organization's GIS. It pairs industry-leading mapping and analytics capabilities with a dedicated Web GIS infrastructure to organize and share your work on any device, anywhere, at any time.
ArcGIS Pro is the essential application for creating and working with spatial data on your desktop. It provides tools to visualize, analyze, compile, and share your data. It is a desktop client, with hardware requirements:
ArcGIS Pro 2.2 system requirements—ArcGIS Pro | ArcGIS Desktop
Now, as far as hardware is concerned, depending on workload, a laptop with a GPU will be more than enough to satisfy most users. your power users will be better suited with a desktop machine, or even a virtual desktop on a server with a GPU and a lighter weight laptop.
Hope this helps.
Jacob is a Sr. Solution Architect for Esri Professional Services and loves conservation planning, woodworking, LEGO, and his dogs.