ASPs, like utility providers, leverage the idea that the same software can be metered out to users and its delivery and management carried out remotely. Unlike utility providers, however, there are already thousands of application providers, so the field needs to be narrowed. The first way to narrow the field is to determine, from your answer to 1. above, whether the task or process is 'core' or 'support'. Choosing an ASP to deliver 'mission critical' processes is very different from choosing an ASP for 'support systems', such as office systems, such as word processing, e-mail, spreadsheets, etc. Unfortunately, ASPs have not yet slotted themselves neatly into the types described here.
Many ASPs appear to be keeping all their options open.
Horizontal' ASPs need market share to offer economies of scale. As your requirements move from left to right of the diagram, competition will be less on price and more on added value services that more closely match your specific needs. Though all ASPs rely on providing 'standard' software, some will offer process templates and pre-configured applications specifically for your business type. Vertical applications may require integration with some of your own systems, for example your finance system, though increasingly they will offer pre-bundled software, to speed the delivery process. The ASP 'supply chain', like your own, has several components.